Dark-bright soliton pairs in nonlocal nonlinear media.

PubMed

Lin, Yuan Yao; Lee, Ray-Kuang

2007-07-09

We study the formation of dark-bright vector soliton pairs in nonlocal Kerr-type nonlinear medium. We show, by analytical analysis and direct numerical calculation, that in addition to stabilize of vector soliton pairs nonlocal nonlinearity also helps to reduce the threshold power for forming a guided bright soliton. With help of the nonlocality, it is expected that the observation of dark-bright vector soliton pairs in experiments becomes more workable.

Vector solitons in femtosecond fibre lasers

NASA Astrophysics Data System (ADS)

Chen, W. C.; Xu, W. C.; Song, F.; Shen, M. C.; Han, D. A.; Chen, L. B.

2008-07-01

Experimental observation of spectral sideband suppression of mode-locked pulses is obtained in an erbium-doped fibre ring laser with nonlinear polarization rotation techniques. This effect may indicate the formation of a vector soliton in accordance with the theoretical work of reference [Phys. Rev. E 74, 046605 (2006)]. The 3 dB spectral bandwidth, the central wavelength and the repetition rate of the vector solitons are 24.41 nm, 1565.14 nm and 12.15 MHz, respectively. Based on the experimental observations, we propose an experimental criterion for the production of vector solitons, with spectral sideband suppression as a sign of the generation of vector solitons.

Scalar-vector soliton fiber laser mode-locked by nonlinear polarization rotation.

PubMed

Wu, Zhichao; Liu, Deming; Fu, Songnian; Li, Lei; Tang, Ming; Zhao, Luming

2016-08-08

We report a passively mode-locked fiber laser by nonlinear polarization rotation (NPR), where both vector and scalar soliton can co-exist within the laser cavity. The mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is first demonstrated and likely to be applicable to various other nonlinear systems. For very large local birefringence, our laser approaches the operation regime of vector soliton lasers, while it approaches scalar soliton fiber lasers under the condition of very small birefringence.

Observation of Polarization-Locked Vector Solitons in an Optical Fiber

NASA Astrophysics Data System (ADS)

Cundiff, S. T.; Collings, B. C.; Akhmediev, N. N.; Soto-Crespo, J. M.; Bergman, K.; Knox, W. H.

1999-05-01

We observe polarization-locked vector solitons in a mode-locked fiber laser. Temporal vector solitons have components along both birefringent axes. Despite different phase velocities due to linear birefringence, the relative phase of the components is locked at +/-π/2. The value of +/-π/2 and component magnitudes agree with a simple analysis of the Kerr nonlinearity. These fragile phase-locked vector solitons have been the subject of much theoretical conjecture, but have previously eluded experimental observation.

Soliton trapping in fiber lasers.

PubMed

Zhao, L M; Tang, D Y; Zhang, H; Wu, X; Xiang, N

2008-06-23

We report on the soliton trapping in a fiber ring laser modelocked with a SESAM. It was observed that solitons along the two orthogonal polarization directions of the cavity with fairly large difference in central frequency and energy could be coupled together to form a group velocity locked vector soliton. In particular, due to that each of the coupled solitons forms its own soliton sidebands, two sets of soliton sidebands could be observed on the vector soliton spectrum. Numerical simulations have well confirmed the experimental observations.

Properties of a vector soliton laser passively mode-locked by a fiber-based semiconductor saturable absorber operating in transmission

NASA Astrophysics Data System (ADS)

Ouyang, Chunmei; Wang, Honghai; Shum, Ping; Fu, Songnian; Wong, Jia Haur; Wu, Kan; Lim, Desmond Rodney Chin Siong; Wong, Vincent Kwok Huei; Lee, Kenneth Eng Kian

2011-01-01

We experimentally demonstrate a passively mode-locked fiber laser employing a fiber-based semiconductor saturable absorber (SSA) operating in transmission. Polarization rotation locked vector solitons are observed in the laser. Due to the intrinsic dynamic feature of the laser, period-doubling of these vector solitons has also been observed. Furthermore, extra spectral sidebands are formed on the optical spectrum, caused by the energy exchange between the two orthogonal polarization components of the vector solitons. By careful reduction of the pump power together with fine adjustment to the cavity birefringence, period-one state can further be obtained. Additionally, the phase noise properties of the vector soliton fiber laser have also been characterized experimentally and analytically.

Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules

NASA Astrophysics Data System (ADS)

Herink, G.; Kurtz, F.; Jalali, B.; Solli, D. R.; Ropers, C.

2017-04-01

Solitons, particle-like excitations ubiquitous in many fields of physics, have been shown to exhibit bound states akin to molecules. The formation of such temporal soliton bound states and their internal dynamics have escaped direct experimental observation. By means of an emerging time-stretch technique, we resolve the evolution of femtosecond soliton molecules in the cavity of a few-cycle mode-locked laser. We track two- and three-soliton bound states over hundreds of thousands of consecutive cavity roundtrips, identifying fixed points and periodic and aperiodic molecular orbits. A class of trajectories acquires a path-dependent geometrical phase, implying that its dynamics may be topologically protected. These findings highlight the importance of real-time detection in resolving interactions in complex nonlinear systems, including the dynamics of soliton bound states, breathers, and rogue waves.

Role of nonthermal electron on the dynamics of relativistic electromagnetic soliton in the interaction of laser-plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rostampooran, Shabnam; Dorranian, Davoud, E-mail: doran@srbiau.ac.ir

A system of nonlinear one-dimensional equations of the electron hydrodynamics with Maxwell's equations was developed to describe electromagnetic (EM) solitons in plasma with nonthermal electrons. Equation of vector potential was derived in relativistic regime by implementing the multiple scales technique, and their solitonic answers were introduced. The allowed regions for bright and dark electromagnetic solitons were discussed in detail. Roles of number density of nonthermal electrons, temperature of electrons, and frequency of fast participate of vector potential on the Sagdeev potential and properties of EM soliton were investigated. Results show that with increasing the number of nonthermal electrons, the amplitudemore » of vector potential of bright solitons increases. By increasing the number of nonthermal electrons, dark EM solitons may be changed to bright solitons. Increasing the energy of nonthermal electrons leads to generation of high amplitude solitons.« less

Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Skryabin, Dmitry V.; Malomed, Boris A.

2018-06-01

We consider the model of fiber-laser cavities near the zero-dispersion point, based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, including the third-order dispersion (TOD) term. It is well known that this model supports stable dissipative solitons. We demonstrate that the same model gives rise to several families of robust bound states of the solitons, which exists only in the presence of the TOD. There are both stationary and dynamical bound states, with oscillating separation between the bound solitons. Stationary states are multistable, corresponding to different values of the separation. With the increase of the TOD coefficient, the bound state with the smallest separation gives rise the oscillatory state through the Hopf bifurcation. Further growth of TOD leads to a bifurcation transforming the oscillatory limit cycle into a strange attractor, which represents a chaotically oscillating dynamical bound state. Families of multistable three- and four-soliton complexes are found too, the ones with the smallest separation between the solitons again ending by a transition to oscillatory states through the Hopf bifurcation.

The dynamics of aloof baby Skyrmions

DOE PAGES

Salmi, Petja; Sutcliffe, Paul

2016-01-25

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)- dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper wemore » present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.« less

The dynamics of aloof baby Skyrmions

NASA Astrophysics Data System (ADS)

Salmi, Petja; Sutcliffe, Paul

2016-01-01

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper we present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salmi, Petja; Sutcliffe, Paul

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)- dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper wemore » present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.« less

Vector dissipative soliton resonance in a fiber laser.

PubMed

Luo, Zhi-Chao; Ning, Qiu-Yi; Mo, Hai-Lan; Cui, Hu; Liu, Jin; Wu, Li-Jun; Luo, Ai-Ping; Xu, Wen-Cheng

2013-04-22

We report on the vector nature of rectangular pulse operating in dissipative soliton resonance (DSR) region in a passively mode-locked fiber laser. Apart from the typical signatures of DSR, the rectangular pulse trapping of two polarization components centered at different wavelengths was observed and they propagated as a group-velocity locked vector soliton. Moreover, the polarization resolved soliton spectra show different spectral distributions. The observed results will enhance the understanding of fundamental physics of DSR phenomenon.

Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers.

PubMed

Sun, Wen-Rong; Liu, De-Yin; Xie, Xi-Yang

2017-04-01

We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.

Vector solitons with locked and precessing states of polarization.

PubMed

Sergeyev, Sergey V; Mou, Chengbo; Rozhin, Aleksey; Turitsyn, Sergei K

2012-11-19

We demonstrate experimentally new families of vector solitons with locked and precessing states of polarization for fundamental and multipulse soliton operations in a carbon nanotube mode-locked fiber laser with anomalous dispersion laser cavity.

Bright-type and dark-type vector solitons of the (2 + 1)-dimensional spatially modulated quintic nonlinear Schrödinger equation in nonlinear optics and Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Wu, Hong-Yu; Jiang, Li-Hong

2018-03-01

We study a (2 + 1) -dimensional N -coupled quintic nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation in nonlinear optics and Bose-Einstein condensate, and obtain bright-type and dark-type vector multipole as well as vortex soliton solutions. When the modulation depth q is fixed as 0 and 1, we can construct vector multipole and vortex solitons, respectively. Based on these solutions, we investigate the form and phase characteristics of vector multipole and vortex solitons.

Soliton excitations and interactions for the three-coupled fourth-order nonlinear Schrödinger equations in the alpha helical proteins

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Tian, Bo; Wang, Yu-Feng; Zhen, Hui-Ling

2015-06-01

Three-coupled fourth-order nonlinear Schrödinger equations describe the dynamics of alpha helical proteins with the interspine coupling at the higher order. Through symbolic computation and binary Bell-polynomial approach, bilinear forms and N-soliton solutions for such equations are constructed. Key point lies in the introduction of auxiliary functions in the Bell-polynomial expression. Asymptotic analysis is applied to investigate the elastic interaction between the two solitons: two solitons keep their original amplitudes, energies and velocities invariant after the interaction except for the phase shifts. Soliton amplitudes are related to the energy distributed in the solitons of the three spines. Overtaking interaction, head-on interaction and bound-state solitons of two solitons are given. Bound states of three bright solitons arise when all of them propagate in parallel. Elastic interaction between the bound-state solitons and one bright soliton is shown. Increase of the lattice parameter can lead to the increase of the soliton velocity, that is, the interaction period becomes shorter. The solitons propagating along the neighbouring spines are found to interact elastically. Those solitons, exhibited in this paper, might be viewed as a possible carrier of bio-energy transport in the protein molecules.

Vector solitons in harmonic mode-locked erbium-doped fiber lasers

NASA Astrophysics Data System (ADS)

Habruseva, Tatiana; Mkhitaryan, Mkhitar; Mou, Chengbo; Rozhin, Aleksey; Turitsyn, Sergei K.; Sergeyev, Sergey V.

2014-05-01

We report experimental study of vector solitons for the fundamental and harmonic mode-locked operation in erbiumdoper fiber lasers with carbon nanotubes based saturable absorbers and anomalous dispersion cavities. We measure evolution of the output pulses polarization and demonstrate vector solitons with various polarization attractors, including locked polarization, periodic polarization switching, and polarization precession.

Conservation laws, bilinear forms and solitons for a fifth-order nonlinear Schrödinger equation for the attosecond pulses in an optical fiber

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chai, Jun; Tian, Bo, E-mail: tian_bupt@163.com; Zhen, Hui-Ling

Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-onmore » and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.« less

Gap solitons in Ginzburg-Landau media.

PubMed

Sakaguchi, Hidetsugu; Malomed, Boris A

2008-05-01

We introduce a model combining basic elements of conservative systems which give rise to gap solitons, i.e., a periodic potential and self-defocusing cubic nonlinearity, and dissipative terms corresponding to the complex Ginzburg-Landau (CGL) equation of the cubic-quintic type. The model may be realized in optical cavities with a periodic transverse modulation of the refractive index, self-defocusing nonlinearity, linear gain, and saturable absorption. By means of systematic simulations and analytical approximations, we find three species of stable dissipative gap solitons (DGSs), and also dark solitons. They are located in the first finite band gap, very close to the border of the Bloch band separating the finite and the semi-infinite gaps. Two species represent loosely and tightly bound solitons, in cases when the underlying Bloch band is, respectively, relatively broad or very narrow. These two families of stationary solitons are separated by a region of breathers. The loosely bound DGSs are accurately described by means of two approximations, which rely on the product of a carrier Bloch function and a slowly varying envelope, or reduce the model to CGL-Bragg equations. The former approximation also applies to dark solitons. Another method, based on the variational approximation, accurately describes tightly bound solitons. The loosely bound DGSs, as well as dark solitons, are mobile, and their collisions are quasielastic.

Decomposition of group-velocity-locked-vector-dissipative solitons and formation of the high-order soliton structure by the product of their recombination.

PubMed

Wang, Xuan; Li, Lei; Geng, Ying; Wang, Hanxiao; Su, Lei; Zhao, Luming

2018-02-01

By using a polarization manipulation and projection system, we numerically decomposed the group-velocity-locked-vector-dissipative solitons (GVLVDSs) from a normal dispersion fiber laser and studied the combination of the projections of the phase-modulated components of the GVLVDS through a polarization beam splitter. Pulses with a structure similar to a high-order vector soliton could be obtained, which could be considered as a pseudo-high-order GVLVDS. It is found that, although GVLVDSs are intrinsically different from group-velocity-locked-vector solitons generated in fiber lasers operated in the anomalous dispersion regime, similar characteristics for the generation of pseudo-high-order GVLVDS are obtained. However, pulse chirp plays a significant role on the generation of pseudo-high-order GVLVDS.

Two different kinds of rogue waves in weakly crossing sea states

NASA Astrophysics Data System (ADS)

Ruban, V. P.

2009-06-01

Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k0±Δk/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle θ between the vectors k0 and Δk , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If θ≲arctan(1/2) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k0 and Δk , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.

Soliton interactions and complexes for coupled nonlinear Schrödinger equations.

PubMed

Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Li, Min; Wang, Pan

2012-03-01

Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the N-CNLS ones (N≥3), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the N-CNLS equations (N>3). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.

Bose polaronic soliton-molecule and vector solitons in PT -symmetric potential

NASA Astrophysics Data System (ADS)

Boudjemâa, Abdelâali

2017-07-01

We study analytically and numerically the properties of polaronic soliton molecules and vector solitons of a trapped Bose-Einstein condensate (BEC)-impurity mixture subjected to a PT -symmetric potential in a quasi one-dimensional geometry employing our time-dependent Hartree-Fock-Bogoliubov equations. Analytical results, based on a variational approach and checked with direct numerical simulations reveal that the width, chirp, the vibration frequency and the profile of impurity solitons are enhanced by varying the strengths of real and imaginary parts of PT -symmetric potential as well as the boson-boson and boson-impurity interaction. We address the impact of the imaginary part of the potential, which represents a gain-loss mechanism, on the dynamics and on the stability of the impurity soliton-molecule. We show that for sufficiently strong complex part of the potential, the single soliton exhibits a snake instability and the molecule destroys analogous to the dissociation of a diatomic molecule. We discuss, on the other hand, the formation of several unusual families of three-component vector solitons in the BEC-impurity mixture. An unconventional dark (D)-bright (B) soliton conversion is found.

Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A and M University at Qatar, P.O. Box 23874 Doha; Belić, Milivoj

2014-12-15

We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number,more » and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.« less

Coherent energy exchange between components of a vector soliton in fiber lasers.

PubMed

Zhang, H; Tang, D Y; Zhao, L M; Xiang, N

2008-08-18

We report on the experimental evidence of four wave mixing (FWM) between the two polarization components of a vector soliton formed in a passively mode-locked fiber laser. Extra spectral sidebands with out-of-phase intensity variation between the polarization resolved soliton spectra was firstly observed, which was identified to be caused by the energy exchange between the two soliton polarization components. Other features of the FWM spectral sidebands and the soliton internal FWM were also experimentally investigated and numerically confirmed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Weicheng; Chen Guojie; Han Dingan

A fibre laser with a SESAM as a passive mode-locker is constructed for obtaining a vector soliton with the Kelly sidebands. The analysis of the peculiarities of the sidebands shows that the polarisation states are nonuniform across the entire pulse spectral profile from the leading edge to the trailing edge. Polarisation filtering effect is proposed to obtain a vector soliton with a uniform polarisation state. It is shown that during the polarisation filtering by a polariser incorporated into the laser cavity, the spectral width of the vector solitons gradually broadens and the pulse power decreases. It is found that atmore » a maximum spectral width and a minimum pulse power, vector solitons with a uniform polarisation state are generated. (nonlinear optical phenomena)« less

Polarization locked vector solitons and axis instability in optical fiber.

PubMed

Cundiff, Steven T.; Collings, Brandon C.; Bergman, Keren

2000-09-01

We experimentally observe polarization-locked vector solitons in optical fiber. Polarization locked-vector solitons use nonlinearity to preserve their polarization state despite the presence of birefringence. To achieve conditions where the delicate balance between nonlinearity and birefringence can survive, we studied the polarization evolution of the pulses circulating in a laser constructed entirely of optical fiber. We observe two distinct states with fixed polarization. This first state occurs for very small values birefringence and is elliptically polarized. We measure the relative phase between orthogonal components along the two principal axes to be +/-pi/2. The relative amplitude varies linearly with the magnitude of the birefringence. This state is a polarization locked vector soliton. The second, linearly polarized, state occurs for larger values of birefringence. The second state is due to the fast axis instability. We provide complete characterization of these states, and present a physical explanation of both of these states and the stability of the polarization locked vector solitons. (c) 2000 American Institute of Physics.

Polarization locked vector solitons and axis instability in optical fiber

NASA Astrophysics Data System (ADS)

Cundiff, Steven T.; Collings, Brandon C.; Bergman, Keren

2000-09-01

We experimentally observe polarization-locked vector solitons in optical fiber. Polarization locked-vector solitons use nonlinearity to preserve their polarization state despite the presence of birefringence. To achieve conditions where the delicate balance between nonlinearity and birefringence can survive, we studied the polarization evolution of the pulses circulating in a laser constructed entirely of optical fiber. We observe two distinct states with fixed polarization. This first state occurs for very small values birefringence and is elliptically polarized. We measure the relative phase between orthogonal components along the two principal axes to be ±π/2. The relative amplitude varies linearly with the magnitude of the birefringence. This state is a polarization locked vector soliton. The second, linearly polarized, state occurs for larger values of birefringence. The second state is due to the fast axis instability. We provide complete characterization of these states, and present a physical explanation of both of these states and the stability of the polarization locked vector solitons.

Manipulation of group-velocity-locked vector dissipative solitons and properties of the generated high-order vector soliton structure.

PubMed

Zhu, S N; Wu, Z C; Fu, S N; Zhao, L M

2018-03-20

Details of various composites of the projections originated from a fundamental group-velocity-locked vector dissipative soliton (GVLVDS) are both experimentally and numerically explored. By combining the projections from the orthogonal polarization components of the GVLVDS, a high-order vector soliton structure with a double-humped pulse profile along one polarization and a single-humped pulse profile along the orthogonal polarization can be observed. Moreover, by de-chirping the composite double-humped pulse, the time separation between the two humps is reduced from 15.36 ps to 1.28 ps, indicating that the frequency chirp of the GVLVDS contributes significantly to the shaping of the double-humped pulse profile.

Multiple polarization states of vector soliton in fiber laser

NASA Astrophysics Data System (ADS)

Chen, Weicheng; Xu, Wencheng; Cao, Hui; Han, Dingan

2007-11-01

Vector soliton is obtained in erbium-doped fiber laser via nonlinear polarization rotation techniques. In experiment, we observe the every 4- and 7-pulse sinusoidal peak modulation. Temporal pulse sinusoidal peak modulation owes to evolution behavior of vector solitons in multiple polarization states. The polarizer in the laser modulates the mode-locked pulses with different polarization states into periodical pulse train intensities modulation. Moreover, the increasing pumping power lead to the appearance of the harmonic pulses and change the equivalent beat length to accelerate the polarization rotation. When the laser cavity length is the n-th multiple ratios to the beat length to maintain the mode-locking, the mode-locked vector soliton is in n-th multiple polarization states, exhibiting every n-pulse sinusoidal peak modulation.

Dynamic trapping of a polarization rotation vector soliton in a fiber laser.

PubMed

Liu, Meng; Luo, Ai-Ping; Luo, Zhi-Chao; Xu, Wen-Cheng

2017-01-15

Ultrafast fiber laser, as a dissipative nonlinear optical system, plays an important role in investigating various nonlinear phenomena and soliton dynamics. Vector features of solitons, including polarization locked and polarization rotation vector solitons (PRVSs), are interesting nonlinear dynamics in ultrafast fiber lasers. Herein, we experimentally reveal the trapping characteristics of PRVSs for the first time, to the best of our best knowledge. We show that, for the conventional soliton trapping in the ultrafast fiber laser, the soliton central wavelengths of the two polarization components are constant at the laser output port. However, it is found that the dynamic trapping can be observed for the PRVS. That is, the peak frequencies along the two orthogonal polarization directions are dynamically alternating, depending on the relative intensities of the two polarization components. The obtained results would further unveil the physical mechanism of PRVSs.

Double-Wall Carbon Nanotube Hybrid Mode-Locker in Tm-doped Fibre Laser: A Novel Mechanism for Robust Bound-State Solitons Generation

NASA Astrophysics Data System (ADS)

Chernysheva, Maria; Bednyakova, Anastasia; Al Araimi, Mohammed; Howe, Richard C. T.; Hu, Guohua; Hasan, Tawfique; Gambetta, Alessio; Galzerano, Gianluca; Rümmeli, Mark; Rozhin, Aleksey

2017-03-01

The complex nonlinear dynamics of mode-locked fibre lasers, including a broad variety of dissipative structures and self-organization effects, have drawn significant research interest. Around the 2 μm band, conventional saturable absorbers (SAs) possess small modulation depth and slow relaxation time and, therefore, are incapable of ensuring complex inter-pulse dynamics and bound-state soliton generation. We present observation of multi-soliton complex generation in mode-locked thulium (Tm)-doped fibre laser, using double-wall carbon nanotubes (DWNT-SA) and nonlinear polarisation evolution (NPE). The rigid structure of DWNTs ensures high modulation depth (64%), fast relaxation (1.25 ps) and high thermal damage threshold. This enables formation of 560-fs soliton pulses; two-soliton bound-state with 560 fs pulse duration and 1.37 ps separation; and singlet+doublet soliton structures with 1.8 ps duration and 6 ps separation. Numerical simulations based on the vectorial nonlinear Schr¨odinger equation demonstrate a transition from single-pulse to two-soliton bound-states generation. The results imply that DWNTs are an excellent SA for the formation of steady single- and multi-soliton structures around 2 μm region, which could not be supported by single-wall carbon nanotubes (SWNTs). The combination of the potential bandwidth resource around 2 μm with the soliton molecule concept for encoding two bits of data per clock period opens exciting opportunities for data-carrying capacity enhancement.

FIBER AND INTEGRATED OPTICS. FIBER WAVEGUIDE DEVICES: Vector solitons in fiber waveguides with a random birefringence

NASA Astrophysics Data System (ADS)

Kivshar', Yu S.; Konotop, V. V.

1990-12-01

A study is made of the propagation of soliton pulses in single-mode fiber waveguides with a birefringence that gives rise to a nonlinear interaction between the polarizations and to a difference between their group velocities. It is shown that a vector soliton decays if a parameter representing the birefringence intensity exceeds a certain critical value. The case when the birefringence can be described by a random function is of special interest. It is demonstrated that fluctuations of the birefringence then split the vector solitons into separate polarizations and the characteristic distance governing such splitting is calculated analytically.

Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays

NASA Astrophysics Data System (ADS)

Meier, Joachim; Hudock, Jared; Christodoulides, Demetrios; Stegeman, George; Silberberg, Y.; Morandotti, R.; Aitchison, J. S.

2003-10-01

We report the first experimental observation of discrete vector solitons in AlGaAs nonlinear waveguide arrays. These self-trapped states are possible through the coexistence of two orthogonally polarized fields and are stable in spite of the presence of four-wave mixing effects. We demonstrate that at sufficiently high power levels the two polarizations lock into a highly localized vector discrete soliton that would have been otherwise impossible in the absence of either one of these two components.

Vector solitons with polarization instability and locked polarization in a fiber laser

NASA Astrophysics Data System (ADS)

Tang, Dingkang; Zhang, Jian-Guo; Liu, Yuanshan

2012-07-01

We investigate the characteristics of vector solitons with and without locked phase velocities of orthogonal polarization components in a specially-designed laser cavity which is formed by a bidirectional fiber loop together with a semiconductor saturable absorber mirror. The characteristics of the two states are compared in the temporal and spectrum domain, respectively. Both of the two states exhibit the characteristic of mode locking while the two orthogonal polarization components are not resolved. However, for the vector soliton with unlocked phase velocities, identical intensity varies after passing through a polarization beam splitter (PBS) outside the laser cavity. Contrary to the polarization rotation locked vector soliton, the intensity does not change periodically. For the polarization-locked vector soliton (PLVS), the identical pulse intensity is still obtained after passing through the PBS and can be observed on the oscilloscope screen after photodetection. A coupler instead of a circulator is integrated in the laser cavity and strong interaction on the polarization resolved spectra of the PLVS is observed. By comparing the two states, we conclude that interaction between the two orthogonal components contributes to the locked phase velocities.

Internal polarization dynamics of vector dissipative-soliton-resonance pulses in normal dispersion fiber lasers.

PubMed

Li, Daojing; Shen, Deyuan; Li, Lei; Tang, Dingyuan; Su, Lei; Zhao, Luming

2018-03-15

Internal polarization dynamics of vector dissipative-soliton-resonance (DSR) pulses in a mode-locked fiber laser are investigated. By utilizing a wave plate analyzer configuration to analyze the special structure of a DSR pulse, we find that polarization state is not uniform across a resonant dissipative soliton. Specifically, although the central plane wave of the resonant dissipative soliton acquires nearly a single fixed polarization, the dissipative fronts feature polarization states that are different and spatially varying. This distinct polarization distribution is maintained while the whole soliton extends with increasing gain. Numerical simulation further confirms the experimental observations.

Double-Wall Carbon Nanotube Hybrid Mode-Locker in Tm-doped Fibre Laser: A Novel Mechanism for Robust Bound-State Solitons Generation

PubMed Central

Chernysheva, Maria; Bednyakova, Anastasia; Al Araimi, Mohammed; Howe, Richard C. T.; Hu, Guohua; Hasan, Tawfique; Gambetta, Alessio; Galzerano, Gianluca; Rümmeli, Mark; Rozhin, Aleksey

2017-01-01

The complex nonlinear dynamics of mode-locked fibre lasers, including a broad variety of dissipative structures and self-organization effects, have drawn significant research interest. Around the 2 μm band, conventional saturable absorbers (SAs) possess small modulation depth and slow relaxation time and, therefore, are incapable of ensuring complex inter-pulse dynamics and bound-state soliton generation. We present observation of multi-soliton complex generation in mode-locked thulium (Tm)-doped fibre laser, using double-wall carbon nanotubes (DWNT-SA) and nonlinear polarisation evolution (NPE). The rigid structure of DWNTs ensures high modulation depth (64%), fast relaxation (1.25 ps) and high thermal damage threshold. This enables formation of 560-fs soliton pulses; two-soliton bound-state with 560 fs pulse duration and 1.37 ps separation; and singlet+doublet soliton structures with 1.8 ps duration and 6 ps separation. Numerical simulations based on the vectorial nonlinear Schr¨odinger equation demonstrate a transition from single-pulse to two-soliton bound-states generation. The results imply that DWNTs are an excellent SA for the formation of steady single- and multi-soliton structures around 2 μm region, which could not be supported by single-wall carbon nanotubes (SWNTs). The combination of the potential bandwidth resource around 2 μm with the soliton molecule concept for encoding two bits of data per clock period opens exciting opportunities for data-carrying capacity enhancement. PMID:28287159

Global structure of five-dimensional fuzzballs

NASA Astrophysics Data System (ADS)

Gibbons, G. W.; Warner, N. P.

2014-01-01

We describe and study families of BPS microstate geometries, namely, smooth, horizonless asymptotically flat solutions to supergravity. We examine these solutions from the perspective of earlier attempts to find solitonic solutions in gravity and show how the microstate geometries circumvent the earlier ‘no-go’ theorems. In particular, we re-analyze the Smarr formula and show how it must be modified in the presence of non-trivial second homology. This, combined with the supergravity Chern-Simons terms, allows the existence of rich classes of BPS, globally hyperbolic, asymptotically flat, microstate geometries whose spatial topology is the connected sum of N copies of S2 × S2 with a ‘point at infinity’ removed. These solutions also exhibit ‘evanescent ergo-regions,’ that is, the non-space-like Killing vector guaranteed by supersymmetry is time-like everywhere except on time-like hypersurfaces (ergo-surfaces) where the Killing vector becomes null. As a by-product of our work, we are able to resolve the puzzle of why some regular soliton solutions violate the BPS bound: their spacetimes do not admit a spin structure.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Chong; Yang, Zhan-Ying, E-mail: zyyang@nwu.edu.cn; Zhao, Li-Chen, E-mail: zhaolichen3@163.com

We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relativemore » background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system. -- Highlights: •Vector rogue wave properties induced by higher-order effects are studied. •A transition between vector rogue waves and solitons is obtained. •The link between the transition and modulation instability (MI) is demonstrated. •The coexistence of vector solitons and breathers coincides with the MI features. •An annihilation phenomenon for the vector two w-shaped solitons is presented.« less

Group-velocity-locked vector soliton molecules in fiber lasers.

PubMed

Luo, Yiyang; Cheng, Jianwei; Liu, Bowen; Sun, Qizhen; Li, Lei; Fu, Songnian; Tang, Dingyuan; Zhao, Luming; Liu, Deming

2017-05-24

Physics phenomena of multi-soliton complexes have enriched the life of dissipative solitons in fiber lasers. By developing a birefringence-enhanced fiber laser, we report the first experimental observation of group-velocity-locked vector soliton (GVLVS) molecules. The birefringence-enhanced fiber laser facilitates the generation of GVLVSs, where the two orthogonally polarized components are coupled together to form a multi-soliton complex. Moreover, the interaction of repulsive and attractive forces between multiple pulses binds the particle-like GVLVSs together in time domain to further form compound multi-soliton complexes, namely GVLVS molecules. By adopting the polarization-resolved measurement, we show that the two orthogonally polarized components of the GVLVS molecules are both soliton molecules supported by the strongly modulated spectral fringes and the double-humped intensity profiles. Additionally, GVLVS molecules with various soliton separations are also observed by adjusting the pump power and the polarization controller.

Localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with time–space modulation

NASA Astrophysics Data System (ADS)

Yao, Yu-Qin; Han, Wei; Li, Ji; Liu, Wu-Ming

2018-05-01

Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

NASA Astrophysics Data System (ADS)

Dasanayaka, Sahan; Atai, Javid

2011-08-01

Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings.

PubMed

Mareeswaran, R Babu; Charalampidis, E G; Kanna, T; Kevrekidis, P G; Frantzeskakis, D J

2014-10-01

In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.

Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media

PubMed Central

Shen, Ming; Gao, Jinsong; Ge, Lijuan

2015-01-01

We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878

Numerical simulations of fast-axis instability of vector solitons in mode-locked fiber lasers.

PubMed

Du, Yueqing; Shu, Xuewen; Cheng, Peiyun

2017-01-23

We demonstrate the fast-axis instability in mode-locked fiber lasers numerically for the first time. We find that the energy of the fast mode will be transferred to the slow mode when the strong pump strength makes the soliton period short. A nearly linearly polarized vector soliton along the slow-axis could be generated under certain cavity parameters. The final polarization of the vector soliton is related to the initial polarization of the seed pulse. Two regimes of energy exchanging between the slow mode and the fast mode are explored and the direction of the energy flow between two modes depends on the phase difference. The dip-type sidebands are found to be intrinsic characteristics of the mode-locked fiber lasers under high pulse energy.

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states

PubMed Central

Afzal, Muhammad Imran; Lee, Yong Tak

2016-01-01

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed. PMID:27966596

Symmetry-breaking instability of quadratic soliton bound states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delque, Michaeel; Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon; Fanjoux, Gil

We study both numerically and experimentally two-dimensional soliton bound states in quadratic media and demonstrate their symmetry-breaking instability. The experiment is performed in a potassium titanyl phosphate crystal in a type-II configuration. The bound state is generated by the copropagation of the antisymmetric fundamental beam locked in phase with the symmetrical second harmonic one. Experimental results are in good agreement with numerical simulations of the nonlinear wave equations.

Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

NASA Astrophysics Data System (ADS)

Mao, Jin-Jin; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-05-01

In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.

Critical density of a soliton gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

El, G. A., E-mail: g.el@lboro.ac.uk

We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg–de Vries soliton gas dynamics. As a by-product of our derivation, we find the speed of sound in the soliton gas with Gaussian spectral distribution function.

Critical density of a soliton gas

NASA Astrophysics Data System (ADS)

El, G. A.

2016-02-01

We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg-de Vries soliton gas dynamics. As a by-product of our derivation, we find the speed of sound in the soliton gas with Gaussian spectral distribution function.

Optical soliton solutions, periodic wave solutions and complexitons of the cubic Schrödinger equation with a bounded potential

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2018-01-01

In this paper, we consider the cubic Schrödinger equation with a bounded potential, which describes the propagation properties of optical soliton solutions. By employing an ansatz method, we precisely derive the bright and dark soliton solutions of the equation. Moreover, we obtain three classes of analytic periodic wave solutions expressed in terms of the Jacobi's elliptic functions including cn ,sn and dn functions. Finally, by using a tanh function method, its complexitons solutions are derived in a very natural way. It is hoped that our results can enrich the nonlinear dynamical behaviors of the cubic Schrödinger equation with a bounded potential.

Polarisation Dynamics of Vector Soliton Molecules in Mode Locked Fibre Laser

PubMed Central

Tsatourian, Veronika; Sergeyev, Sergey V.; Mou, Chengbo; Rozhin, Alex; Mikhailov, Vitaly; Rabin, Bryan; Westbrook, Paul S.; Turitsyn, Sergei K.

2013-01-01

Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning. PMID:24193374

Polarisation Dynamics of Vector Soliton Molecules in Mode Locked Fibre Laser

NASA Astrophysics Data System (ADS)

Tsatourian, Veronika; Sergeyev, Sergey V.; Mou, Chengbo; Rozhin, Alex; Mikhailov, Vitaly; Rabin, Bryan; Westbrook, Paul S.; Turitsyn, Sergei K.

2013-11-01

Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning.

Bound states and interactions of vortex solitons in the discrete Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mejía-Cortés, C.; Soto-Crespo, J. M.; Vicencio, Rodrigo A.; Molina, Mario I.

2012-08-01

By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions have a symmetric amplitude profile and two different topological charges. We also observe the dynamical formation of a variety of “bound-state” solutions composed of two or more of these vortex solitons. All of these stable composite structures persist in the conservative cubic limit for high values of their power content.

Soliton polarization rotation in fiber lasers

NASA Astrophysics Data System (ADS)

Afanasjev, V. V.

1995-02-01

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

Supermodes in Coupled Multi-Core Waveguide Structures

DTIC Science & Technology

2016-04-01

and therefore can be treated as linear polarization (LP) modes. In essence, the LP modes are scalar approximations of the vector mode fields and contain...field, including the discovery of optical discrete solitons , Bragg and vector solitons in fibers, nonlinear surface waves, and the discovery of self...increased for an isolated core, it can guide high-order modes. For optical fibers with low re- fractive index contrast, the vector modes are weakly guided

Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion

NASA Astrophysics Data System (ADS)

Gromov, E. M.; Malomed, B. A.; Tyutin, V. V.

2018-01-01

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton.

Induced solitons formed by cross-polarization coupling in a birefringent cavity fiber laser.

PubMed

Zhang, H; Tang, D Y; Zhao, L M; Tam, H Y

2008-10-15

We report on the experimental observation of induced solitons in a passively mode-locked fiber ring laser with a birefringence cavity. Owing to the cross coupling between the two orthogonal polarization components of the laser, it was found that if a soliton was formed along one cavity polarization axis, a weak soliton was also induced along the orthogonal polarization axis, and depending on the net cavity birefringence, the induced soliton could have either the same or different center wavelengths to that of the inducing soliton. Moreover, the induced soliton always had the same group velocity as that of the inducing soliton. They formed a vector soliton in the cavity. Numerical simulations confirmed the experimental observations.

Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes

NASA Astrophysics Data System (ADS)

Wong, Jia Haur; Wu, Kan; Liu, Huan Huan; Ouyang, Chunmei; Wang, Honghai; Aditya, Sheel; Shum, Ping; Fu, Songnian; Kelleher, E. J. R.; Chernov, A.; Obraztsova, E. D.

2011-04-01

Polarization Rotation Locked Vector Solitons (PRLVSs) are experimentally observed for the first time in a fiber ring laser passively mode-locked by a single-wall carbon nanotube (SWCNT) saturable absorber. Period-doubling of these solitons at certain birefringence values has also been observed. We show that fine adjustment to the intracavity birefringence can swing the PRLVSs from period-doubled to period-one state without simultaneous reduction in the pump strength. The timing jitter for both states has also been measured experimentally and discussed analytically using the theoretical framework provided by the Haus model.

Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

PubMed

Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

2015-04-01

The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

Bilinear forms and soliton solutions for a fourth-order variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin

2016-01-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple-dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.

Quantum lattice representations for vector solitons in external potentials

NASA Astrophysics Data System (ADS)

Vahala, George; Vahala, Linda; Yepez, Jeffrey

2006-03-01

A quantum lattice algorithm is developed to examine the effect of an external potential well on exactly integrable vector Manakov solitons. It is found that the exact solutions to the coupled nonlinear Schrodinger equations act like quasi-solitons in weak potentials, leading to mode-locking, trapping and untrapping. Stronger potential wells will lead to the emission of radiation modes from the quasi-soliton initial conditions. If the external potential is applied to that particular mode polarization, then the radiation will be trapped within the potential well. The algorithm developed leads to a finite difference scheme that is unconditionally stable. The Manakov system in an external potential is very closely related to the Gross-Pitaevskii equation for the ground state wave functions of a coupled BEC state at T=0 K.

Mode-locking peculiarities in an all-fiber erbium-doped ring ultrashort pulse laser with a highly-nonlinear resonator

NASA Astrophysics Data System (ADS)

Dvoretskiy, Dmitriy A.; Sazonkin, Stanislav G.; Kudelin, Igor S.; Orekhov, Ilya O.; Pnev, Alexey B.; Karasik, Valeriy E.; Denisov, Lev K.

2017-12-01

Today ultrashort pulse (USP) fiber lasers are in great demand in a frequency metrology field, THz pulse spectroscopy, optical communication, quantum optics application, etc. Therefore mode-locked (ML) fiber lasers have been extensively investigated over the last decade due the number of scientific, medical and industrial applications. It should be noted, that USP fiber lasers can be treated as an ideal platform to expand future applications due to the complex ML nonlinear dynamics in a laser resonator. Up to now a series of novel ML regimes have been investigated e.g. self-similar pulses, noise-like pulses, multi-bound solitons and soliton rain generation. Recently, we have used a highly nonlinear germanosilicate fiber (with germanium oxides concentration in the core 50 mol. %) inside the resonator for more reliable and robust launching of passive mode-locking based on the nonlinear polarization evolution effect in fibers. In this work we have measured promising and stable ML regimes such as stretched pulses, soliton rain and multi-bound solitons formed in a highly-nonlinear ring laser and obtained by intracavity group velocity dispersion (GVD) variation in slightly negative region. As a result, we have obtained the low noise ultrashort pulse generation with duration < 250 fs (more than 20 bound pulses when obtained multi-bound soliton generation with intertemporal width 5 ps) at a repetition rate 11.3 MHz (with signal-to-noise ratio at fundamental frequency > 59 dB) and relative intensity noise <-101 dBc / Hz.

Bright-dark soliton pairs in a self-mode locking fiber laser

NASA Astrophysics Data System (ADS)

Meng, Yichang; Zhang, Shumin; Li, Hongfei; Du, Juan; Hao, Yanping; Li, Xingliang

2012-06-01

We have experimentally observed bright-dark soliton pairs in an erbium-doped fiber ring laser for the first time. This approach is different from the vector dark domain wall solitons which separate the two orthogonal linear polarization eigenstates of the laser emission. In our laser, the bright-dark soliton pairs can co-exist in any one polarization state. Numerical simulations based on the coupled complex Ginzburg-Landau equations have confirmed the experimental results.

New derivation of soliton solutions to the AKNS2 system via dressing transformation methods

NASA Astrophysics Data System (ADS)

Assunção, A. de O.; Blas, H.; da Silva, M. J. B. F.

2012-03-01

We consider certain boundary conditions supporting soliton solutions in the generalized nonlinear Schrödinger equation (AKNSr) (r = 1, 2). Using the dressing transformation (DT) method and the related tau functions, we study the AKNSr system for the vanishing, (constant) non-vanishing and the mixed boundary conditions, and their associated bright, dark and bright-dark N-soliton solutions, respectively. Moreover, we introduce a modified DT related to the dressing group in order to consider the free-field boundary condition and derive generalized N dark-dark solitons. As a reduced submodel of the AKNSr system, we study the properties of the focusing, defocusing and mixed focusing-defocusing versions of the so-called coupled nonlinear Schrödinger equation (r-CNLS), which has recently been considered in many physical applications. We have shown that two-dark-dark-soliton bound states exist in the AKNS2 system, and three- and higher-dark-dark-soliton bound states cannot exist. The AKNSr (r ⩾ 3) extension is briefly discussed in this approach. The properties and calculations of some matrix elements using level-one vertex operators are outlined. Dedicated to the memory of S S Costa

Describing the strongly interacting quark-gluon plasma through the Friedberg-Lee model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shu Song; Li Jiarong; Institute of Particle Physics, Hua-Zhong Normal University, Wuhan 430079

2010-10-15

The Friedberg-Lee (FL) model is studied at finite temperature and density. The soliton solutions of the FL model in the deconfinement phase transition are solved and thoroughly discussed for certain boundary conditions. We indicate that the solitons before and after the deconfinement have different physical meanings: the soliton before deconfinement represents hadrons, while the soliton after the deconfinement represents the bound state of quarks which leads to a strongly interacting quark-gluon plasma phase. The corresponding phase diagram is given.

Soliton-impurity interaction in two Ablowitz-Ladik chains with different coupling

NASA Astrophysics Data System (ADS)

Kamburova, R. S.; Primatarowa, M. T.

2014-12-01

The interaction of solitons with point defects in a system of coupled Ablowitz- Ladik (AL) chains is studied numerically. The system is a discrete analog of coupled nonlinear Schrodinger equations. Two types of interchain coupling are investigated: one which admits reduction of the system to the standard integrable AL model (dispersive coupling) and one which couples opposite sites of the chains and does not admit reduction to the AL model (nondispersive coupling). The action of the two coupling types is additive and they can compensate each other in some cases. We have obtained that the single-peak bound soliton-defect solution (attractive impurity) is stable against perturbations, while the double-peak bound soliton-defect solution (repulsive impurity) is unstable and can be easily destroyed. Linear point defects do not influence the period of energy transfer and it is close to the period for the homogeneous case.

Directional Characteristics of Inner Shelf Internal Tides

DTIC Science & Technology

2007-06-01

Figure 18. YD 202-206 Current vector plot of significant events. Significant events include internal tidal bores, solibores, and solitons . The upper...Events (Bores, Solibores, and Solitons ): Upper column leading-edge cross-shore current velocity and cross-shore wind regression. The small ellipse...Significant Events (Bores, Solibores, and Solitons ): Upper column leading-edge along-shore current velocity and along-shore wind regression. The small

Wavelength tunable L Band polarization-locked vector soliton fiber laser based on SWCNT-SA and CFBG

NASA Astrophysics Data System (ADS)

Yan, Yaxi; Wang, Jiaqi; Wang, Liang; Cheng, Zhenzhou

2018-04-01

Wavelength tunable L-Band polarization-locked vector soliton fiber laser based on single-walled carbon nanotube saturable absorber (SWCNT-SA) and chirped fiber Bragg grating (CFBG) is presented for the first time. By inserting the SWCNT-SA into an all-fiber laser cavity, polarization-locked vector solitons (PLVS) are obtained. The CFBG glued on a plastic cantilever is used for wavelength tuning. By mechanically bending the cantilever, the center wavelength of the PLVS pulses can be continuously tuned from 1606.8 nm to 1614 nm, while the polarization-locked state is kept stable. The properties and dynamics of PLVSs are experimentally investigated and stable PLVS operation including high-order PLVSs is demonstrated. The pulse width and repetition rate are 7.06 ps and 11.9 MHz at a wavelength of 1611 nm, respectively. This work demonstrates the feasibility of using polarization-insensitive CFBG to realize wavelength tuning in PLVS fiber laser.

Spatial vector soliton and its collisions in isotropic self-defocusing Kerr media.

PubMed

Radhakrishnan, R; Aravinthan, K

2007-06-01

A fairly general form of the two-component (dark-dark) vector one-soliton solution of the integrable coupled nonlinear Schrödinger equation (Manakov model) with self-defocusing nonlinearity is obtained by using the Hirota method. It couples two dark components with the same envelope width, envelope speed, and envelope trough location using two complex arbitrary parameters not only in the envelope amplitude but also in the complex modulation. Although it has the freedom to change its pulse width without affecting its speed, it can also tune its grayness (depth of the pulse relative to background) without disturbing the envelope width and speed. The variations in peak power against the depth of localization of two dark components are investigated with and without a parametric restriction. The collision between many dark-dark vector solitons has also been studied by constructing a multisoliton solution with more free parameters.

Multi-soliton interaction of a generalized Schrödinger-Boussinesq system in a magnetized plasma

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Chai, Jun; Wu, Xiao-Yu; Guo, Yong-Jiang

2017-04-01

Under investigation in this paper is a generalized Schrödinger-Boussinesq system, which describes the stationary propagation of coupled upper-hybrid waves and magnetoacoustic waves in a magnetized plasma. Bilinear forms, one-, two- and three-soliton solutions are derived by virtue of the Hirota method and symbolic computation. Propagation and interaction for the solitons are illustrated graphically: Coefficients β1^{} and β2^{} can affect the velocities and propagation directions of the solitary waves. Amplitude, velocity and shape of the one solitary wave keep invariant during the propagation, implying that the transport of the energy is stable in the upper-hybrid and magnetoacoustic waves, and amplitude of the upper-hybrid wave is bigger than that of the magnetoacoustic wave. For the upper-hybrid and magnetoacoustic waves, head-on, overtaking and bound-state interaction between the two solitary waves are asymptotically depicted, respectively, indicating that the interaction between the two solitary waves is elastic. Elastic interaction between the bound-state soliton and a single one soliton is also displayed, and interaction among the three solitary waves is all elastic.

Silica-coated gold nanorods as saturable absorber for bound-state pulse generation in a fiber laser with near-zero dispersion

NASA Astrophysics Data System (ADS)

Wang, Xude; Luo, Aiping; Luo, Zhichao; Liu, Meng; Zou, Feng; Zhu, Yanfang; Xue, Jianping; Xu, Wencheng

2017-11-01

We presented a bound-state operation in a fiber laser with near-zero anomalous dispersion based on a silica-coated gold nanorods (GNRs@SiO2) saturable absorber (SA). Using a balanced twin detector measurement technique, the modulation depth and nonsaturable loss of the GNRs@SiO2 SA were measured to be approximately 3.5% and 39.3%, respectively. By virtue of the highly nonlinear effect of the GNRs@SiO2 SA, the bound-state pulses could be easily observed. Besides the lower-order bound-state pulses with two, three, and four solitons, the higher-order bound states with up to 12 solitons were also obtained in the laser cavity. The pulse profiles of the higher-order bound states were further reconstructed theoretically. The experimental results would give further insight towards understanding the complex nonlinear dynamics of bound-state pulses in fiber lasers.

Switchable thulium-doped fiber laser from polarization rotation vector to scalar soliton

NASA Astrophysics Data System (ADS)

Wu, Zhichao; Fu, Songnian; Jiang, Kai; Song, Jue; Li, Huizi; Tang, Ming; Shum, Ping; Liu, Deming

2016-10-01

We experimentally demonstrate switchable temporal soliton generation from a thulium-doped fiber laser (TDFL), using carbon nanotubes as the mode-locker. With the help of residual polarization dependent loss of a wavelength division multiplexer, a weak nonlinear polarization rotation (NPR) effect can be achieved within the laser cavity, which may provide joint contribution for passive mode-locking operation. By finely adjusting the polarization to alter the strength of NPR-based saturable absorption, the TDFL either approaches the operation regime of scalar soliton with strong NPR effect, or generates polarization rotation locked vector soliton (PRLVS) with weak NPR effect. The scalar solitons and PRLVSs possess 3-dB optical spectrum bandwidth of 2.2 nm and 2 nm, pulse-width of 1.8 ps and 2 ps, respectively. Moreover, the PRLVSs demonstrate a typical energy exchange between two polarized components on optical spectra and a period-doubling feature in time domain. Such operation principle can also be used in 1550 nm band fiber lasers and other nonlinear systems.

Switchable thulium-doped fiber laser from polarization rotation vector to scalar soliton

PubMed Central

Wu, Zhichao; Fu, Songnian; Jiang, Kai; Song, Jue; Li, Huizi; Tang, Ming; Shum, Ping; Liu, Deming

2016-01-01

We experimentally demonstrate switchable temporal soliton generation from a thulium-doped fiber laser (TDFL), using carbon nanotubes as the mode-locker. With the help of residual polarization dependent loss of a wavelength division multiplexer, a weak nonlinear polarization rotation (NPR) effect can be achieved within the laser cavity, which may provide joint contribution for passive mode-locking operation. By finely adjusting the polarization to alter the strength of NPR-based saturable absorption, the TDFL either approaches the operation regime of scalar soliton with strong NPR effect, or generates polarization rotation locked vector soliton (PRLVS) with weak NPR effect. The scalar solitons and PRLVSs possess 3-dB optical spectrum bandwidth of 2.2 nm and 2 nm, pulse-width of 1.8 ps and 2 ps, respectively. Moreover, the PRLVSs demonstrate a typical energy exchange between two polarized components on optical spectra and a period-doubling feature in time domain. Such operation principle can also be used in 1550 nm band fiber lasers and other nonlinear systems. PMID:27708427

Switchable thulium-doped fiber laser from polarization rotation vector to scalar soliton.

PubMed

Wu, Zhichao; Fu, Songnian; Jiang, Kai; Song, Jue; Li, Huizi; Tang, Ming; Shum, Ping; Liu, Deming

2016-10-06

We experimentally demonstrate switchable temporal soliton generation from a thulium-doped fiber laser (TDFL), using carbon nanotubes as the mode-locker. With the help of residual polarization dependent loss of a wavelength division multiplexer, a weak nonlinear polarization rotation (NPR) effect can be achieved within the laser cavity, which may provide joint contribution for passive mode-locking operation. By finely adjusting the polarization to alter the strength of NPR-based saturable absorption, the TDFL either approaches the operation regime of scalar soliton with strong NPR effect, or generates polarization rotation locked vector soliton (PRLVS) with weak NPR effect. The scalar solitons and PRLVSs possess 3-dB optical spectrum bandwidth of 2.2 nm and 2 nm, pulse-width of 1.8 ps and 2 ps, respectively. Moreover, the PRLVSs demonstrate a typical energy exchange between two polarized components on optical spectra and a period-doubling feature in time domain. Such operation principle can also be used in 1550 nm band fiber lasers and other nonlinear systems.

Infiltrated bunch of solitons in Bi-doped frequency-shifted feedback fibre laser operated at 1450 nm

PubMed Central

Rissanen, Joona; Korobko, Dmitry A.; Zolotovsky, Igor O.; Melkumov, Mikhail; Khopin, Vladimir F.; Gumenyuk, Regina

2017-01-01

Mode-locked fibre laser as a dissipative system is characterized by rich forms of soliton interaction, which take place via internal energy exchange through noisy background in the presence of dispersion and nonlinearity. The result of soliton interaction was either stationary-localized or chaotically-oscillated soliton complexes, which have been shown before as stand-alone in the cavity. Here we report on a new form of solitons complex observed in Bi-doped mode-locked fibre laser operated at 1450 nm. The solitons are arranged in two different group types contemporizing in the cavity: one pulse group propagates as bound solitons with fixed phase relation and interpulse position eventuated in 30 dB spectrum modulation depth; while the other pulses form a bunch with continuously and chaotically moving solitons. The article describes both experimental and theoretical considerations of this effect. PMID:28281677

All-fiber polarization locked vector soliton laser using carbon nanotubes.

PubMed

Mou, C; Sergeyev, S; Rozhin, A; Turistyn, S

2011-10-01

We report an all-fiber mode-locked erbium-doped fiber laser (EDFL) employing carbon nanotube (CNT) polymer composite film. By using only standard telecom grade components, without any complex polarization control elements in the laser cavity, we have demonstrated polarization locked vector solitons generation with duration of ~583 fs, average power of ~3 mW (pulse energy of 118 pJ) at the repetition rate of ~25.7 MHz. © 2011 Optical Society of America

Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals

PubMed Central

Poznanski, R. R.; Cacha, L. A.; Ali, J.; Rizvi, Z. H.; Yupapin, P.; Salleh, S. H.; Bandyopadhyay, A.

2017-01-01

A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge ‘soakage’ is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge ‘soakage’) have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell’s equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current. PMID:28880876

Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals.

PubMed

Poznanski, R R; Cacha, L A; Ali, J; Rizvi, Z H; Yupapin, P; Salleh, S H; Bandyopadhyay, A

2017-01-01

A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge 'soakage' is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge 'soakage') have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell's equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current.

Quasi-Phasematched Nonlinear Optics: Materials and Devices

DTIC Science & Technology

2007-04-16

the soliton energy in pump, signal and idler waves as a function of the final wave- vector mismatch in the chirped QPM gratings. We see good agreement...devices including OP-GaAs devices for broadband optical parametric generation (OPG) at mid-infrared wavelengths, bulk PPLN devices for soliton ...Carrasco, and L. Torner,"Engineering of multi-color spatial solitons with chirped-period quasi-phase-matching gratings in optical parametric amplification

Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Sun, Yan

2018-01-01

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

Bright-dark and dark-dark solitons for the coupled cubic-quintic nonlinear Schrödinger equations in a twin-core nonlinear optical fiber

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Chai, Han-Peng

2017-11-01

In this paper, we investigate the coupled cubic-quintic nonlinear Schrödinger equations, which can describe the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in a twin-core nonlinear optical fiber. Through the Kadomtsev-Petviashvili hierarchy reduction, we present the bright-dark and dark-dark soliton solutions in terms of the Grammian for such equations. With the help of analytic and graphic analysis, head-on and overtaking elastic interactions between the two solitons are presented, as well as the bound-state solitons. Particularly, we find the inelastic interaction between the bright-dark two solitons. One of the electromagnetic fields presents the V-shape profile, while the other one presents the Y-shape profile.

Localised Nonlinear Waves in the Three-Component Coupled Hirota Equations

NASA Astrophysics Data System (ADS)

Xu, Tao; Chen, Yong

2017-10-01

We construct the Lax pair and Darboux transformation for the three-component coupled Hirota equations including higher-order effects such as third-order dispersion, self-steepening, and stimulated Raman scattering. A special vector solution of the Lax pair with 4×4 matrices for the three-component Hirota system is elaborately generated, based on this vector solution, various types of mixed higher-order localised waves are derived through the generalised Darboux transformation. Instead of considering various arrangements of the three potential functions q1, q2, and q3, here, the same combination is considered as the same type solution. The first- and second-order localised waves are mainly discussed in six mixed types: (1) the hybrid solutions degenerate to the rational ones and three components are all rogue waves; (2) two components are hybrid solutions between rogue wave (RW) and breather (RW+breather), and one component is interactional solution between RW and dark soliton (RW+dark soliton); (3) two components are RW+dark soliton, and one component is RW+bright soliton; (4) two components are RW+breather, and one component is RW+bright soliton; (5) two components are RW+dark soliton, and one component is RW+bright soliton; (6) three components are all RW+breather. Moreover, these nonlinear localised waves merge with each other by increasing the absolute values of two free parameters α, β. These results further uncover some striking dynamic structures in the multicomponent coupled system.

Inelastic Vector Soliton Collisions: A Lattice-Based Quantum Representation

DTIC Science & Technology

2004-01-01

components in these orthogonal polarizations will travel at slightly different speeds. It can be shown (Lakshmanan & Kanna 2001) that the slowly varying...media. Phys. Rev. E 58, 6752-6758. Kivshar, Y. S. & Agrawal, G. P. 2003 Optical solitons. Academic. Lakshmanan, M. & Kanna , T. 2001 Shape changing

Group velocity locked vector dissipative solitons in a high repetition rate fiber laser

NASA Astrophysics Data System (ADS)

Luo, Yiyang; Li, Lei; Liu, Deming; Sun, Qizhen; Wu, Zhichao; Xu, Zhilin; Tang, Dingyuan; Fu, Songnian; Zhao, Luming

2016-08-01

Vectorial nature of dissipative solitons (DSs) with high repetition rates is studied for the first time in a normal-dispersion fiber laser. Despite the fact that the formed DSs are strongly chirped and the repetition rate is greater than 100 MHz, polarization locked and polarization rotating group velocity locked vector DSs can be formed under 129.3 MHz fundamental mode-locking and 258.6 MHz harmonic mode-locking of the fiber laser, respectively. The two orthogonally polarized components of these vector DSs possess distinctly different central wavelengths and travel together at the same group velocity in the laser cavity, resulting in a gradual spectral edge and small steps on the optical spectra, which can be considered as an auxiliary indicator of the group velocity locked vector DSs.

Bright-dark soliton solutions for the (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger system in a graded-index waveguide

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Liu, Lei

2017-04-01

Under investigation in this paper is the (2+1)-dimensional coupled nonlinear Schrödinger (NLS) system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. Through a similarity transformation, we convert that system into a set of the integrable defocusing (1+1)-dimensional coupled NLS equations, and subsequently construct the bright-dark soliton solutions for the original system which are converted from the ones of the latter set. With the graphic analysis, we discuss the soliton propagation and collision with r(t), which is related to the nonlinear, profile and gain/loss coefficients. When r(t) is a constant, one soliton propagates with the amplitude, width and velocity unvaried, while velocity and width of the one soliton can be affected, and two solitons possess the elastic collision; When r(t) is a linear function, velocity and width of the one soliton varies with t increasing, and collision of the two solitons is altered. Besides, bound-state solitons are seen.

Ultrafast Optics: Vector Cavity Fiber Lasers - Physics and Technology

DTIC Science & Technology

2016-06-14

with a quasi- vector cavity both numerically and experimentally. It is expected that through the study a deep and comprehensive understanding on the...799-801, Jun. 1997. 31. L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen , "Noise-like pulse in a gain-guided soliton fiber laser," Opt...solitons in a ring fiber laser," Optics Communications 281 (22), 5614 (2008). 110. L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen , "Noise-like

Ultrafast Optics: Vector Cavity Laser - Physics and Technology

DTIC Science & Technology

2016-06-14

with a quasi- vector cavity both numerically and experimentally. It is expected that through the study a deep and comprehensive understanding on the...799-801, Jun. 1997. 31. L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen , "Noise-like pulse in a gain-guided soliton fiber laser," Opt...solitons in a ring fiber laser," Optics Communications 281 (22), 5614 (2008). 110. L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen , "Noise-like

Ultrafast Optics - Vector Cavity Lasers: Physics and Technology

DTIC Science & Technology

2016-06-14

with a quasi- vector cavity both numerically and experimentally. It is expected that through the study a deep and comprehensive understanding on the...799-801, Jun. 1997. 31. L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen , "Noise-like pulse in a gain-guided soliton fiber laser," Opt...solitons in a ring fiber laser," Optics Communications 281 (22), 5614 (2008). 110. L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen , "Noise-like

Bilinearization of the generalized coupled nonlinear Schrödinger equation with variable coefficients and gain and dark-bright pair soliton solutions.

PubMed

Chakraborty, Sushmita; Nandy, Sudipta; Barthakur, Abhijit

2015-02-01

We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.

Polariton solitons and nonlinear localized states in a one-dimensional semiconductor microcavity

NASA Astrophysics Data System (ADS)

Chen, Ting-Wei; Cheng, Szu-Cheng

2018-01-01

This paper presents numerical studies of cavity polariton solitons (CPSs) in a resonantly pumped semiconductor microcavity with an imbedded spatial defect. In the bistable regime of the well-known homogeneous polariton condensate, with proper incident wave vector and pump strength, bright and/or dark cavity solitons can be found in the presence of a spatially confined potential. The minimum pump strength required to observe the CPSs or nonlinear localized states in this parametric pump scheme is therefore reported.

N-dark-dark solitons for the coupled higher-order nonlinear Schrödinger equations in optical fibers

NASA Astrophysics Data System (ADS)

Zhang, Hai-Qiang; Wang, Yue

2017-11-01

In this paper, we construct the binary Darboux transformation on the coupled higher-order dispersive nonlinear Schrödinger equations in optical fibers. We present the N-fold iterative transformation in terms of the determinants. By the limit technique, we derive the N-dark-dark soliton solutions from the non-vanishing background. Based on the obtained solutions, we find that the collision mechanisms of dark vector solitons exhibit the standard elastic collisions in both two components.

Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Malomed, Boris A., E-mail: malomed@post.tau.ac.il

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate thatmore » one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.« less

Dissipative vector soliton in a dispersion-managed fiber laser with normal dispersion.

PubMed

Wang, Siming; Fan, Xuliang; Zhao, Luming; Wang, Yong; Tang, Dingyuan; Shen, Deyuan

2014-12-10

We numerically study the vector dynamics of dissipative solitons (DSs) in a 2 μm dispersion-managed fiber laser mode locked by a semiconductor saturable absorber mirror and operated in the normal dispersion regime. It is shown that the effective gain bandwidth is crucial for the DS generation. The steep spectral edges of DSs are the consequence of the interaction among the normal dispersion, fiber nonlinearity, gain and loss, and gain dispersion effect, etc. We numerically duplicate the experimental results and further explore the vector features of the generated DSs. Two DSs formed along the two orthogonal polarization directions which, incoherently coupled with each other, could propagate in the birefringent cavity with the same group velocity.

Field-induced metastability of the modulation wave vector in a magnetic soliton lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, M.; Peng, J.; Hong, T.

We present magnetic-field-induced metastability of the magnetic soliton lattice in a bilayer ruthenate Ca 3(Ru 1–xFe x) 2O 7(x=0.05) through single-crystal neutron diffraction study. We show that the incommensurability of the modulation wave vector at zero field strongly depends on the history of magnetic field at low temperature, and that the equilibrium ground state can be achieved by warming above a characteristic temperature T g~37K. Lastly, we suggest that such metastability might be associated with the domain wall pinning by the magnetic Fe dopants.

Field-induced metastability of the modulation wave vector in a magnetic soliton lattice

DOE PAGES

Zhu, M.; Peng, J.; Hong, T.; ...

2017-04-19

We present magnetic-field-induced metastability of the magnetic soliton lattice in a bilayer ruthenate Ca 3(Ru 1–xFe x) 2O 7(x=0.05) through single-crystal neutron diffraction study. We show that the incommensurability of the modulation wave vector at zero field strongly depends on the history of magnetic field at low temperature, and that the equilibrium ground state can be achieved by warming above a characteristic temperature T g~37K. Lastly, we suggest that such metastability might be associated with the domain wall pinning by the magnetic Fe dopants.

Bright-dark solitons for a set of the general coupled nonlinear Schrödinger equations in a birefringent fiber

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Sun, Yan

2017-11-01

Under investigation in this paper is the coupled nonlinear Schrödinger equations with the four-wave mixing term, which describe the optical solitons in a birefringent fiber. Via the Kadomtsev-Petviashvili hierarchy reduction, we obtain the N-bright-dark soliton solutions in terms of the Gram determinant. Propagation and interaction of the solitons corresponding to the electric fields in the two orthogonal polarizations are discussed and presented graphically. We find that the one bright-dark soliton possesses the periodic oscillation and exhibits the breather-like profile, which is different from that in the previous literature. Besides, for the one soliton, we observe that the larger velocity leads to the fiercer oscillation. Elastic interactions including the head-on and overtaking interactions between the two bright-dark solitons are demonstrated. Particularly, we find the oblique inelastic interaction between the two bright-dark solitons, which possess the V-shape profile in the zero background component and the Y-shape profile in the nonzero background component. Besides, we present two cases of the bound-state solitons. For the one case, the two solitons interact with each other all the time along a direction and for the other case, the resonance phenomenon is raised.

Influence of electromagnetic field on soliton-mediated charge transport in biological systems.

PubMed

Brizhik, Larissa

2015-01-01

It is shown that electromagnetic fields affect dynamics of Davydov's solitons which provide charge transport processes in macromolecules during metabolism of the system. There is a resonant frequency of the field at which it can cause the transition of electrons from bound soliton states into delocalised states. Such decay of solitons reduces the effectiveness of charge transport, and, therefore, inhibits redox processes. Solitons radiate their own electromagnetic field of characteristic frequency determined by their average velocity. This self-radiated field leads to synchronization of soliton dynamics and charge transport processes, and is the source of the coherence in the system. Exposition of the system to the oscillating electromagnetic field of the frequency, which coincides with the eigen-frequency of solitons can enhance eigen-radiation of solitons, and, therefore, will enhance synchronization of charge transpor, stimulate the redox processes and increase coherence in the system. Electromagnetic oscillating field causes also ratchet phenomenon of solitons, i.e., drift of solitons in macromolecules in the presence of unbiased periodic field. Such additional drift enhances the charge transport processes. It is shown that temperature facilitates the ratchet drift. In particular, temperature fluctuations lead to the lowering of the critical value of the intensity and period of the field, above which the drift of solitons takes place. Moreover, there is a stochastic resonance in the soliton dynamics in external electromagnetic fields. This means, that there is some optimal temperature at which the drift of solitons is maximal.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharma, Arvind, E-mail: arvindsharma230771@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com

We investigate the interaction of optical vector soliton with a symmetric thin-film gallium-silica waveguide structure using the equivalent particle theory. The relevant nonlinear Schrodinger equation has been solved by the method of phase plane analysis. The analysis shows beam break up into transmitted, reflected and nonlinear surface waves at the interface. The stability properties of the solitons so formed have been discussed.

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

NASA Astrophysics Data System (ADS)

Dingwall, R. J.; Edmonds, M. J.; Helm, J. L.; Malomed, B. A.; Öhberg, P.

2018-04-01

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.

Vector mesons in the Nambu-Jona-Lasinio model

NASA Astrophysics Data System (ADS)

Schüren, C.; Döring, F.; Ruiz Arriola, E.; Goeke, K.

1993-12-01

We investigate solitonic solutions with baryon number equal to one of the semi-bosonized SU(2) Nambu-Jona-Lasinio model including σ -, π -, ρ -, A 1- and ω-mesons both on the chiral circle ( σ2r) + π2( r) = f2π) and beyond it ( σ2( r) + π2( r) ≠ f2π). The action is treated in the mesonic and baryonic sector in the leading order of the large- Nc expansion (one-quark-loop approximation). The UV-divergent real part of the effective action is rendered finite using different gauge-invariant regularization methods (Pauli-Villars and proper time). The parameters of the model are fixed in two different ways: either approximately by a heat kernel expansion of the effective action up to second order or by an exact calculation of the mesonic on-shell masses. This leaves the constituent quark mass as the only free parameter of the model. In the solitonic sector we pay special attention to the way the Wick rotation from euclidean space back to Minkowski space has to be performed. We get solitonic solutions from hedgehoglike field configurations on the chiral circle for a wide range of couplings. We also find that if the chiral-circle constraint is relaxed vector mesons provide stable solitonic solutions. Moreover, whether the baryon number is carried by the valence quarks or by the Dirac sea depends strongly on the particular values of the constituent quark mass. We also study the low-energy limit of the model and its connection to chiral perturbation theory. To this end a covariant-derivative expansion is performed in the presence of external fields. After integrating out the scalar, vector and axial degrees of freedom this leads to the corresponding low-energy parameters as e.g. pion radii and some threshold parameters for pion-pion scattering. Vector mesons provide a natural explanation for an axial coupling constant at the quark level gAQ lower than one. However, we find for the gAN of the nucleon noticeable deviations from the non-relativistic quark model prediction g AN = {5}/{3}g AQ. For the values of the parameters where solitons are found, pionic radii come out to be too small. Finally, the relation of the present model to other chiral soliton models as well as some effective lagrangians is displayed.

Twisted sigma-model solitons on the quantum projective line

NASA Astrophysics Data System (ADS)

Landi, Giovanni

2018-04-01

On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather involved, the use of the positivity and the bound by the topological term lead to self-duality equations (thus yielding twisted noncommutative sigma-model solitons, or instantons). We present explicit nontrivial solutions on the quantum projective line.

Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Gopi, D.

2017-11-01

We investigate the nonlinear spin dynamics of a spin polarized current driven anisotropic ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction (DMI) under the influence of electromagnetic wave (EMW) propagating along the axis of the nanowire. The magnetization dynamics and electromagnetic wave propagation in the ferromagnetic nanowire with weak anti-symmetric interaction is governed by a coupled vector Landau-Lifshitz-Gilbert and Maxwell's equations. These coupled nonlinear vector equations are recasted into the extended derivative nonlinear Schrödinger (EDNLS) equation in the framework of reductive perturbation method. As it is well known, the modulational instability is a precursor for the emergence of localized envelope structures of various kinds, we compute the instability criteria for the weak ferromagnetic nanowire through linear stability analysis. Further, we invoke the homogeneous balance method to construct kink and anti-solitonic like electromagnetic (EM) soliton profiles for the EDNLS equation. We also explore the appreciable effect of the anti-symmetric weak interaction on the magnetization components of the propagating EM soliton. We find that the combination of spin-polarized current and the anti-symmetric DMI have a profound effect on the propagating EMW in a weak ferromagnetic nanowire. Thus, the anti-symmetric DMI in a spin polarized current driven ferromagnetic nanowire supports the lossless propagation of EM solitons, which may have potential applications in magnetic data storage devices.

Conversion of the high-mode solitons in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Zhang, Xiaping

2017-01-01

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder-Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince-Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.

Polariton condensation in solitonic gap states in a one-dimensional periodic potential

PubMed Central

Tanese, D.; Flayac, H.; Solnyshkov, D.; Amo, A.; Lemaître, A.; Galopin, E.; Braive, R.; Senellart, P.; Sagnes, I.; Malpuech, G.; Bloch, J.

2013-01-01

Manipulation of nonlinear waves in artificial periodic structures leads to spectacular spatial features, such as generation of gap solitons or onset of the Mott insulator phase transition. Cavity exciton–polaritons are strongly interacting quasiparticles offering large possibilities for potential optical technologies. Here we report their condensation in a one-dimensional microcavity with a periodic modulation. The resulting mini-band structure dramatically influences the condensation process. Contrary to non-modulated cavities, where condensates expand, here, we observe spontaneous condensation in localized gap soliton states. Depending on excitation conditions, we access different dynamical regimes: we demonstrate the formation of gap solitons either moving along the ridge or bound to the potential created by the reservoir of uncondensed excitons. We also find Josephson oscillations of gap solitons triggered between the two sides of the reservoir. This system is foreseen as a building block for polaritonic circuits, where propagation and localization are optically controlled and reconfigurable. PMID:23612290

Baby Skyrme models without a potential term

NASA Astrophysics Data System (ADS)

Ashcroft, Jennifer; Haberichter, Mareike; Krusch, Steffen

2015-05-01

We develop a one-parameter family of static baby Skyrme models that do not require a potential term to admit topological solitons. This is a novel property as the standard baby Skyrme model must contain a potential term in order to have stable soliton solutions, though the Skyrme model does not require this. Our new models satisfy an energy bound that is linear in terms of the topological charge and can be saturated in an extreme limit. They also satisfy a virial theorem that is shared by the Skyrme model. We calculate the solitons of our new models numerically and observe that their form depends significantly on the choice of parameter. In one extreme, we find compactons while at the other there is a scale invariant model in which solitons can be obtained exactly as solutions to a Bogomolny equation. We provide an initial investigation into these solitons and compare them with the baby Skyrmions of other models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Foster, David; Sutcliffe, Paul

Recent results suggest that multi-Skyrmions stabilized by {omega} mesons have very similar properties to those stabilized by the Skyrme term. In this paper we present the results of a detailed numerical investigation of a (2+1)-dimensional analogue of this situation. Namely, we compute solitons in an O(3) {sigma} model coupled to a massive vector meson and compare the results to baby Skyrmions, which are solitons in an O(3) {sigma} model including a Skyrme term. We find that multisolitons in the vector meson model are surprisingly similar to those in the baby Skyrme model, and we explain this correspondence using a simplemore » derivative expansion.« less

High precision computing with charge domain devices and a pseudo-spectral method therefor

NASA Technical Reports Server (NTRS)

Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor); Fijany, Amir (Inventor); Zak, Michail (Inventor)

1997-01-01

The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

A New Class of Almost Ricci Solitons and Their Physical Interpretation

PubMed Central

2016-01-01

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u, μ, p, α, η, σ ij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems. PMID:28044145

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Vlijm, R.; Ganahl, M.; Fioretto, D.; Brockmann, M.; Haque, M.; Evertz, H. G.; Caux, J.-S.

2015-12-01

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time-evolution fits on the displacements. The time-evolved block decimation algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Fioretto, Davide; Vljim, Rogier; Ganahl, Martin; Brockmann, Michael; Haque, Masud; Evertz, Hans-Gerd; Caux, Jean-Sébastien

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The TEBD algorithm allows for the study of scattering displacements from spin-block states, showing similar displacement scattering features.

On the possibility of observing bound soliton pairs in a wave-breaking-free mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Martel, G.; Chédot, C.; Réglier, V.; Hideur, A.; Ortaç, B.; Grelu, Ph.

2007-02-01

On the basis of numerical simulations, we explain the formation of the stable bound soliton pairs that were experimentally reported in a high-power mode-locked ytterbium fiber laser [Opt. Express 14, 6075 (2006)], in a regime where wave-breaking-free operation is expected. A fully vectorial model allows one to rigorously reproduce the nonmonotonic nature for the nonlinear polarization effect that generally limits the power scalability of a single-pulse self-similar regime. Simulations show that a self-similar regime is not fully obtained, although positive linear chirps and parabolic spectra are always reported. As a consequence, nonvanishing pulse tails allow distant stable binding of highly-chirped pulses.

Multi-pulse operation of a dissipative soliton fibre laser based on nonlinear polarisation rotation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, H L; Wang, X L; Zhou, P

We report an experimental observation of multiple dissipative soliton (DS) operation states in an all-normal-dispersion passively mode-locked Yb-doped fibre laser, including DS bound and oscillating states. In the bound state, multiple DSs up to 11 can coexist in the cavity. In the oscillating state, the DSs' movements are not purely random and three typical states are generalised and illustrated. A single-pulse mode-locked state is established at a high pump power by carefully adjusting the polarisation controllers. The broad spectrum indicates that it may be noise-like pulses, which can serve as a pump to generate a supercontinuum. (control of laser radiationmore » parameters)« less

Spherical solitons in Earth'S mesosphere plasma

NASA Astrophysics Data System (ADS)

Annou, K.; Annou, R.

2016-01-01

Soliton formation in Earth's mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev-Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

Spherical solitons in Earth’S mesosphere plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Annou, K., E-mail: kannou@cdta.dz; Annou, R.

2016-01-15

Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

Research on polarization vector characteristics in a microfiber-based graphene fiber laser

NASA Astrophysics Data System (ADS)

Han, Mengmeng; Zhang, Shumin; Li, Xingliang; Han, Huiyun; Liu, Jingmin; Yan, Dan

2016-11-01

We experimentally investigated the polarization vector characteristics in an Er-doped fiber laser based on graphene that was deposited on microfiber. A variety of dynamic states, including polarization locked fundamental soliton, and polarization domain wall square pulses and their harmonic mode locked counterparts have all been observed with different pump powers and polarization states. These results indicated that the microfiber-based graphene not only could act as a saturable absorber but also could provide high nonlinearity, which is favorable for the cross coupling between the two orthogonal polarization components. It was worth to mention that it is the first time to obtain the polarization domain wall solitons in a mode locked fiber laser.

Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities

NASA Astrophysics Data System (ADS)

Choi, Mi-Ran; Hundertmark, Dirk; Lee, Young-Ran

2017-10-01

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities; they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold λcr such that minimizers for this variational problem exist if their power is bigger than λcr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of Hundertmark and Lee [J. Nonlinear Sci. 22, 1-38 (2012) and Commun. Math. Phys. 309(1), 1-21 (2012)].

Generation of bound states of pulses in a SESAM mode-locked Cr:ZnSe laser

NASA Astrophysics Data System (ADS)

Bu, Xiangbao; Shi, Yuhang; Xu, Jia; Li, Huijuan; Wang, Pu

2018-06-01

We report on the generation of bound states of pulses in a SESAM mode-locked Cr:ZnSe laser around 2415 nm. A thulium-doped double-clad fiber laser at 1908 nm was used as the pump source. Bound states with various pulse separations at different dispersion regimes were obtained. Especially, in the anomalous dispersion regime, vibrating bound state of solitons exhibiting an evolving phase was obtained.

Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Danaila, I.; Khamehchi, M. A.; Gokhroo, V.; Engels, P.; Kevrekidis, P. G.

2016-11-01

Multicomponent Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work [C. Qu, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 116, 160402 (2016), 10.1103/PhysRevLett.116.160402], the notion of magnetic solitons has been introduced. Here we examine a variant of this concept in the form of vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates (BECs). We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and intercomponent repulsion. Armed with this more general conceptual framework, we expand the notion of such states to higher dimensions presenting the possibility of both vortex-antidark states and ring-antidark-ring (dark soliton) states. We perform numerical continuation studies, investigate the existence of these states, and examine their stability using the method of Bogoliubov-de Gennes analysis. Dark-antidark and vortex-antidark states are found to be stable for broad parametric regimes. In the case of ring dark solitons, where the single-component ring state is known to be unstable, the vector entity appears to bear a progressively more and more stabilizing role as the intercomponent coupling is increased.

Topological Switching and Orbiting Dynamics of Colloidal Spheres Dressed with Chiral Nematic Solitons

PubMed Central

Porenta, T.; Čopar, S.; Ackerman, P. J.; Pandey, M. B.; Varney, M. C. M.; Smalyukh, I. I.; Žumer, S.

2014-01-01

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that “dress” the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed. PMID:25477195

Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons.

PubMed

Porenta, T; Copar, S; Ackerman, P J; Pandey, M B; Varney, M C M; Smalyukh, I I; Žumer, S

2014-12-05

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that "dress" the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Diffraction-induced instability of coupled dark solitary waves.

PubMed

Assanto, Gaetano; MacNeil, J Michael L; Smyth, Noel F

2015-04-15

We report on a novel instability arising from the propagation of coupled dark solitary beams governed by coupled defocusing nonlinear Schrödinger equations. Considering dark notches on backgrounds with different wavelengths, hence different diffraction coefficients, we find that the vector dark soliton solution is unstable to radiation modes. Using perturbation theory and numerical integration, we demonstrate that the component undergoing stronger diffraction radiates away, leaving a single dark soliton in the other mode/wavelength.

Stability of matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

2010-08-01

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

Birefringent Fiber Devices and Lasers

NASA Astrophysics Data System (ADS)

Theimer, James Prentice

1995-01-01

This thesis presents the results of numerical simulations of mode-locked figure eight lasers and their components: fiber amplifiers and nonlinear optical loop mirrors (NOLMs). The computations were designed to study pulse evolution in optical amplifiers and NOLMs with periodic repetition of these elements. Since fiber laser systems also include birefringent fiber, the effects of fiber birefringence was incorporated into the simulations. My studies of pulse amplification in non-birefringent amplifiers show pulse breakup when their energies exceed 4.5 fundamental soliton energies. In birefringent fibers pulse breakup is also found, but the two orthogonally polarized pulses propagate together. I find that their behavior is related to the properties of a vector soliton. I found that vector waves have close to unity transmission through a birefringent NOLM, but the pulse shape is distorted. This shape distortion reduces subsequent transmissions through the NOLM. The energy required for peak transmission of the pulse is predicted by the theory based on vector solitons. The same theory also predicted the low intensity transmission. The performance of the NOLM with birefringent fiber could not be improved by altering the polarization state of the pulse from linear polarization; the polarization controller introduced pulse distortion that resulted in excessive loss. I found an instability in the steady-state operation of the figure eight laser, which is due to pulse reshaping during propagation in the amplifier section. To remove this instability I introduced the concept of dispersion balancing; by increasing the dispersion in the amplifier section, the pulse can propagate nearly as a fundamental soliton in both the amplifier and the NOLM sections of the laser. This eliminated a major source of dispersive wave shedding and allowed the laser operation to become independent of the amplifier length. Sidebands were found on the pulse spectrum and their maxima corresponded well with the periodic resonance model.

Standing electromagnetic solitons in hot ultra-relativistic electron-positron plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heidari, E., E-mail: ehphys75@iaubushehr.ac.ir; Aslaninejad, M.; Eshraghi, H.

2014-03-15

Using a one-dimensional self-consistent fluid model, we investigate standing relativistic bright solitons in hot electron-positron plasmas. The positron dynamics is taken into account. A set of nonlinear coupled differential equations describing the evolution of electromagnetic waves in fully relativistic two-fluid plasma is derived analytically and solved numerically. As a necessary condition for the existence of standing solitons the system should be relativistic. For the case of ultra-relativistic plasma, we investigate non-drifting bright solitary waves. Detailed discussions of the acceptable solutions are presented. New single hump non-trivial symmetric solutions for the scalar potential were found, and single and multi-nodal symmetric andmore » anti-symmetric solutions for the vector potential are presented. It is shown that for a fixed value of the fluid velocity excited modes with more zeros in the profile of the vector potential show a higher magnitude for the scalar potential. An increase in the plasma fluid velocity also increases the magnitude of the scalar potential. Furthermore, the Hamiltonian and the first integral of the system are given.« less

Darboux transformation of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization

NASA Astrophysics Data System (ADS)

Xu, Tao; Chen, Yong

2018-04-01

In this paper, we extend the one-component Gross-Pitaevskii (GP) equation to the two-component coupled GP system including damping term, linear and parabolic density profiles. The Lax pair with nonisospectral parameter and infinitely-many conservation laws of this coupled GP system are presented. Actually, the Darboux transformation (DT) for this kind of nonautonomous system is essentially different from the autonomous case. Consequently, we construct the DT of the coupled GP equations, besides, nonautonomous multi-solitons, one-breather and the first-order rogue wave are also obtained. Various kinds of one-soliton solution are constructed, which include stationary one-soliton and nonautonomous one-soliton propagating along the negative (positive) direction of x-axis. The interaction of two solitons and two-soliton bound state are demonstrated respectively. We get the nonautonomous one-breather on a curved background and this background is completely controlled by the parameter β. Using a limiting process, the nonautonomous first-order rogue wave can be obtained. Furthermore, some dynamic structures of these analytical solutions are discussed in detail. In addition, the multi-component generalization of GP equations are given, then the corresponding Lax pair and DT are also constructed.

Solitonic and chaotic behaviors of a (3+1)-dimensional nonlinear Schrödinger equation in a magnetized electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Chai, Jun

2015-05-01

In a magnetized e-p-i plasma with two-electron temperatures, the (3+1)-dimensional nonlinear Schrödinger equation for the ion-acoustic envelope solitons is hereby investigated. Bright and dark soliton solutions are both obtained. It is found that the soliton amplitude is inversely related to P, Q and R, with P, Q and R respectively as the coefficients of the dispersive term, nonlinear term and combined effect of the transverse perturbation and magnetic field. Head-on interactions are displayed, and with Q and R decreasing, can be transferred into the overtaking ones. Bright bound-state solitons are obtained, and the interaction period decreases with Q increasing. Both the head-on and overtaking interactions between the two dark solitons are displayed, and such a head-on interaction can be transformed into the overtaking one with R increasing. Upon the introduction of the external perturbation, the developed and weak chaos are observed. Phase projections and power spectra are presented. Difference between the two chaotic motions roots in the inequality between the nonlinear and perturbed terms. Developed chaos can be weakened with Q decreasing, or with the frequency of external perturbation increasing.

Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions

NASA Astrophysics Data System (ADS)

Pathak, Pallabi; Sharma, Sumita K.; Nakamura, Y.; Bailung, H.

2017-12-01

The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations.

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

NASA Astrophysics Data System (ADS)

Thies, Michael

2017-05-01

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1  +  1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-de Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.

Fast and slowly evolving vector solitons in mode-locked fibre lasers.

PubMed

Sergeyev, Sergey V

2014-10-28

We report on a new vector model of an erbium-doped fibre laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. Unlike the previous models, it accounts for the vector nature of the interaction between an optical field and an erbium-doped active medium, slow relaxation dynamics of erbium ions, linear birefringence in a fibre, linear and circular birefringence of a laser cavity caused by in-cavity polarization controller and light-induced anisotropy caused by elliptically polarized pump field. Interplay of aforementioned factors changes coherent coupling of two polarization modes at a long time scale and so results in a new family of vector solitons (VSs) with fast and slowly evolving states of polarization. The observed VSs can be of interest in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetization in data storage devices and many other areas. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

Spontaneous symmetry breaking in coupled parametrically driven waveguides.

PubMed

Dror, Nir; Malomed, Boris A

2009-01-01

We introduce a system of linearly coupled parametrically driven damped nonlinear Schrödinger equations, which models a laser based on a nonlinear dual-core waveguide with parametric amplification symmetrically applied to both cores. The model may also be realized in terms of parallel ferromagnetic films, in which the parametric gain is provided by an external field. We analyze spontaneous symmetry breaking (SSB) of fundamental and multiple solitons in this system, which was not studied systematically before in linearly coupled dissipative systems with intrinsic nonlinearity. For fundamental solitons, the analysis reveals three distinct SSB scenarios. Unlike the standard dual-core-fiber model, the present system gives rise to a vast bistability region, which may be relevant to applications. Other noteworthy findings are restabilization of the symmetric soliton after it was destabilized by the SSB bifurcation, and the existence of a generic situation with all solitons unstable in the single-component (decoupled) model, while both symmetric and asymmetric solitons may be stable in the coupled system. The stability of the asymmetric solitons is identified via direct simulations, while for symmetric and antisymmetric ones the stability is verified too through the computation of stability eigenvalues, families of antisymmetric solitons being entirely unstable. In this way, full stability maps for the symmetric solitons are produced. We also investigate the SSB bifurcation of two-soliton bound states (it breaks the symmetry between the two components, while the two peaks in the shape of the soliton remain mutually symmetric). The family of the asymmetric double-peak states may decouple from its symmetric counterpart, being no longer connected to it by the bifurcation, with a large portion of the asymmetric family remaining stable.

Dark-bright soliton pairs: Bifurcations and collisions

NASA Astrophysics Data System (ADS)

Katsimiga, G. C.; Kevrekidis, P. G.; Prinari, B.; Biondini, G.; Schmelcher, P.

2018-04-01

The statics, stability, and dynamical properties of dark-bright soliton pairs are investigated here, motivated by applications in a homogeneous two-component repulsively interacting Bose-Einstein condensate. One of the intraspecies interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra and interspecies repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. This bifurcation interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intraspecies variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.

Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Wen-Rong; Tian, Bo, E-mail: tian_bupt@163.com; Jiang, Yan

2014-04-15

Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us tomore » investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.« less

Phases and approximations of baryonic popcorn in a low-dimensional analogue of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2015-07-01

The Sakai-Sugimoto model is the most pre-eminent model of holographic QCD, in which baryons correspond to topological solitons in a five-dimensional bulk spacetime. Recently it has been shown that a single soliton in this model can be well approximated by a flat-space self-dual Yang-Mills instanton with a small size, although studies of multi-solitons and solitons at finite density are currently beyond numerical computations. A lower-dimensional analogue of the model has also been studied in which the Sakai-Sugimoto soliton is replaced by a baby Skyrmion in three spacetime dimensions with a warped metric. The lower dimensionality of this model means that full numerical field calculations are possible, and static multi-solitons and solitons at finite density were both investigated, in particular the baryonic popcorn phase transitions at high densities. Here we present and investigate an alternative lower-dimensional analogue of the Sakai-Sugimoto model in which the Sakai-Sugimoto soliton is replaced by an O(3)-sigma model instanton in a warped three-dimensional spacetime stabilized by a massive vector meson. A more detailed range of baryonic popcorn phase transitions are found, and the low-dimensional model is used as a testing ground to check the validity of common approximations made in the full five-dimensional model, namely approximating fields using their flat-space equations of motion, and performing a leading order expansion in the metric.

CALL FOR PAPERS: Optical solitons

NASA Astrophysics Data System (ADS)

Drummond, P. D.; Haelterman, Marc; Vilaseca, R.

2003-06-01

A topical issue of Journal of Optics B: Quantum and Semiclassical Optics will be devoted to recent advances in optical solitons. The topics to be covered will include, but are not limited to: bulletProperties, control and dynamics of temporal solitons bulletProperties, control and dynamics of spatial solitons bulletCavity solitons in passive and active resonators bulletThree-dimensional spatial solitons bulletDark, bright, grey solitons; interface dynamics bulletCompound or vector solitons; incoherent solitons bulletLight and matter solitons in BEC bulletNonlinear localized structures in microstructured and nanostructured materials (photonic crystals, etc) bulletAngular momentum effects associated with localized light structures; vortex solitons bulletQuantum effects associated with localized light structures bulletInteraction of solitons with atoms and other media bulletApplications of optical solitons The DEADLINE for submission of contributions is 31 July 2003 to allow the topical issue to appear in about February 2004. All papers will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. Submissions should ideally be in either standard LaTeX form or Microsoft Word. There are no page charges for publication. In addition to the usual 50 free reprints, the corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should if possible be submitted electronically at www.iop.org/journals/jopb. or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Dr Claire Bedrock (Publisher), Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All contributions should be accompanied by a readme file or covering letter, quoting `JOPB topical issue - Optical Solitons', giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. We look forward to receiving your contribution to this topical issue.

The role of solitons in charge and energy transfer in 1D molecular chains

NASA Astrophysics Data System (ADS)

Ivić , Zoran

1998-03-01

The idea that polarons and solitons could play the crucial role in the transport processes in biological structures, has been critically reexamined on the basis of the general theory of self-trapping phenomena. The criteria which enable one to determine conditions for the existence and stability of polarons and solitons and to determine their character, in dependence of the values of the basic physical parameters of the system, were formulated. Validity of the so-called Davydov's soliton model was discussed on the basis of these criteria. It was found that the original Davydov's proposal, based upon the idea of the soliton creation due to the single excitation (particle, vibron, etc.) self-trapping, cannot explain the intramolecular energy transfer in α-helix and acetanilide. However, Davydov theory is flexible enough to describe the single electron transfer in some systems (α-helix and acetanilide for example). In the many-particle systems, dressing effect, due to the quantum nature of phonons, may cause the creation of the bound states of the several excitons in the molecular chain. The possibility of creation of the soliton states of this type is discussed for the simple Fröhlich's one-dimensional model. The regions of the system parameter space where different mechanisms dominate the behaviour of such entities are characterized.

Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Xu, Tao; Sun, Fu-Wei; Zhang, Yi; Li, Juan

2014-01-01

It is known that the Kadomtsev-Petviashvili (KP) equation can be decomposed into the first two members of the coupled Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy by the binary non-linearization of Lax pairs. In this paper, we construct the N-th iterated Darboux transformation (DT) for the second- and third-order m-coupled AKNS systems. By using together the N-th iterated DT and Cramer's rule, we find that the KPII equation has the unreduced multi-component Wronskian solution and the KPI equation admits a reduced multi-component Wronskian solution. In particular, based on the unreduced and reduced two-component Wronskians, we obtain two families of fully-resonant line-soliton solutions which contain arbitrary numbers of asymptotic solitons as y → ∓∞ to the KPII equation, and the ordinary N-soliton solution to the KPI equation. In addition, we find that the KPI line solitons propagating in parallel can exhibit the bound state at the moment of collision.

Investigation of the Nicole model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adam, C.; Sanchez-Guillen, J.; Vazquez, R.A.

2006-05-15

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP{sup 1} Lagrangian density to the non-integer power (3/2) - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behavior to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemimore » model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.« less

The NRL Program on Electroactive Polymers.

DTIC Science & Technology

1980-09-15

cell of a point in an aggregate involves selecting the smallest cell formed by planes perpendicularly bisecting all the point to neighbor vectors . Such...plane perpendicular to the interatomic vector is located nearer the smaller atom by bisecting the distance between the sur- faces of spheres whose...density waves (and consequent novel excitations such as solitons (6)). The physical structure as well as the chemical bonding of such polymeric

Ferromagnetic Switching of Knotted Vector Fields in Liquid Crystal Colloids.

PubMed

Zhang, Qiaoxuan; Ackerman, Paul J; Liu, Qingkun; Smalyukh, Ivan I

2015-08-28

We experimentally realize polydomain and monodomain chiral ferromagnetic liquid crystal colloids that exhibit solitonic and knotted vector field configurations. Formed by dispersions of ferromagnetic nanoplatelets in chiral nematic liquid crystals, these colloidal ferromagnets exhibit spontaneous long-range alignment of magnetic dipole moments of individual platelets, giving rise to a continuum of the magnetization field M(r). Competing effects of surface confinement and chirality prompt spontaneous formation and enable the optical generation of localized twisted solitonic structures with double-twist tubes and torus knots of M(r), which exhibit a strong sensitivity to the direction of weak magnetic fields ∼1  mT. Numerical modeling, implemented through free energy minimization to arrive at a field-dependent three-dimensional M(r), shows a good agreement with experiments and provides insights into the torus knot topology of observed field configurations and the corresponding physical underpinnings.

Dispersive MHD Shock Properties and Interactions with Alfven Solitons

NASA Astrophysics Data System (ADS)

Hamilton, R.; Toll, K.; Ellis, C.

2017-12-01

The weakly nonlinear, weakly dispersive limit of Hall MHD with resistivity for 1D waves travelling nearly parallel to the ambient magnetic field reduces to the derivative nonlinear Schrödinger-Burgers (DNLSB) equation. This model equation describes the coupling between the Alfvenic and magnetosonic modes for a low b plasma. Without dissipation this model equation reduces to the DNLS which can be solved as an initial value problem using the Inverse Scattering Transformation through which the nonlinear component of the magnetic field profile can be represented as a combination of one-parameter bright and dark solitons as well as two-parameter solitons. The one-parameter solitons are constrained to travel at speeds ranging between the Alfvenic and magnetosonic characteristic speeds of the ambient field. We have found that these one-parameter solitons are effectively bound to a 1-2 Fast Shock and will pass back and forth across the shock until they are damped away with no apparent effect on the Fast Shock. A similar mechanism is expected for a sufficiently compressive Intermediate Shock as it arises simply from two effects: damping of a one-parameter soliton causes it to speed up and, if it does not damp away, it will eventually overtake the shock; passing forwards through a compressive shock the decrease of the field strength leads to a slowing of the soliton. We also discuss an extension of results [C. F. Kennel, R. D. Blandford, C. C. Wu, Phys. Fluids B 2(2), 1990] related to the time dependence of Intermediate Shocks in the presence of dispersion.

The Multidimensional Solitons in a Plasma: Structure Stability and Dynamics

DTIC Science & Technology

2003-07-20

ax(8 H’ / 8u), (2) into GKP (Generalized Kadomtsev - Petviashvili ) class where of equations , and in the case when 13 4nnT / B 2 << 1 1 1 for 6) < OB= eB...that the soliton elastic collisions can lead to formation of complex structures including the multisoliton bound states. 1. Basic equations Eq. (1) with...scribed by equation 2. Stability of 2D and 3D solutions atu + A(t,u)u =f, f= K 0X Ajudx, (1) To study stability of the GKP equation solutions, we =a 2

Rational Degenerations of M-Curves, Totally Positive Grassmannians and KP2-Solitons

NASA Astrophysics Data System (ADS)

Abenda, Simonetta; Grinevich, Petr G.

2018-03-01

We establish a new connection between the theory of totally positive Grassmannians and the theory of M-curves using the finite-gap theory for solitons of the KP equation. Here and in the following KP equation denotes the Kadomtsev-Petviashvili 2 equation [see (1)], which is the first flow from the KP hierarchy. We also assume that all KP times are real. We associate to any point of the real totally positive Grassmannian Gr^{tp} (N,M) a reducible curve which is a rational degeneration of an M-curve of minimal genus {g=N(M-N)} , and we reconstruct the real algebraic-geometric data á la Krichever for the underlying real bounded multiline KP soliton solutions. From this construction, it follows that these multiline solitons can be explicitly obtained by degenerating regular real finite-gap solutions corresponding to smooth M-curves. In our approach, we rule the addition of each new rational component to the spectral curve via an elementary Darboux transformation which corresponds to a section of a specific projection Gr^{tp} (r+1,M-N+r+1)\\mapsto Gr^{tp} (r,M-N+r).

Soliton-like defects in nematic liquid crystal thin layers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chuvyrov, A. N.; Krekhov, A. P.; Lebedev, Yu. A., E-mail: lebedev@anrb.ru

The nonsingular soliton-like defects in plane nematic liquid crystal (NLC) layers and spherical NLC drops are experimentally detected and studied when the interaction of NLC molecules with a bounding surface is varied. The dynamics and the annihilation of nonsingular defects of opposite signs on a plane surface are investigated. Periodic transformations of the soliton-like defects in NLC drops in an electric field are detected. The theory of elasticity is used to show that the surface energy taken into account in the total free energy of NLC in the case of weak anchoring leads to the possibility of nonsingular solutions ofmore » a director equilibrium equation. The calculated pictures of director distribution in a plane NLC layer and in a spherical NLC drop characterized by weak surface anchoring agree well with the results of polarized light optical observations.« less

Nonlinear dynamics of the 3D FMS and Alfven wave beams propagating in plasma of ionosphere and magnetosphere

NASA Astrophysics Data System (ADS)

Belashov, Vasily

We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega>{k_{yz}}(2,) v_{x}$<

Static axisymmetric Einstein equations in vacuum: Symmetry, new solutions, and Ricci solitons

NASA Astrophysics Data System (ADS)

Akbar, M. M.; MacCallum, M. A. H.

2015-09-01

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the action of the group can be effected algebraically on any solution of the system. This enables one to construct particular one-parameter extended families of axisymmetric static solutions and cylindrical gravitational wave solutions from old ones, in a simpler way than most solution-generation techniques, including the prescription given by Ernst for this system. As examples, we obtain the families that generalize the Schwarzschild solution and the C -metric. These in effect superpose a Levi-Civita cylindrical solution on the seeds. Exploiting a correspondence between static solutions of Einstein's equations and Ricci solitons (self-similar solutions of the Ricci flow), this also enables us to construct new steady Ricci solitons.

Detection of Accelerating Targets in Clutter Using a De-Chirping Technique

DTIC Science & Technology

2014-06-01

Academy, also in Canberra, working on the the- ory and simulation of spatial optical solitons and light-induced optical switching in nonlinear...signal gain in the receiver. UNCLASSIFIED 1 DSTO–RR–0399 UNCLASSIFIED target along the velocity vector , or equivalently by radar platform. The change of...the tracker uses range rate in its track initiation logic. (2) Lateral acceleration perpendicular to the velocity vector - the target is turning and

Elliptic-type soliton combs in optical ring microresonators

NASA Astrophysics Data System (ADS)

Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.

2018-03-01

Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary-wave solutions, and the numerical results are in very good agreement with the collective-coordinate approach.

Theoretical nuclear physics

NASA Astrophysics Data System (ADS)

Rost, E.; Shephard, J. R.

1992-08-01

This report discusses the following topics: Exact 1-loop vacuum polarization effects in 1 + 1 dimensional QHD; exact 1-fermion loop contributions in 1 + 1 dimensional solitons; exact scalar 1-loop contributions in 1 + 3 dimensions; exact vacuum calculations in a hyper-spherical basis; relativistic nuclear matter with self-consistent correlation energy; consistent RHA-RPA for finite nuclei; transverse response functions in the (triangle)-resonance region; hadronic matter in a nontopological soliton model; scalar and vector contributions to (bar p)p yields (bar lambda)lambda reaction; 0+ and 2+ strengths in pion double-charge exchange to double giant-dipole resonances; and nucleons in a hybrid sigma model including a quantized pion field.

Phases of kinky holographic nuclear matter

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew; Sutcliffe, Paul; Zamaklar, Marija

2016-10-01

Holographic QCD at finite baryon number density and zero temperature is studied within the five-dimensional Sakai-Sugimoto model. We introduce a new approximation that models a smeared crystal of solitonic baryons by assuming spatial homogeneity to obtain an effective kink theory in the holographic direction. The kink theory correctly reproduces a first order phase transition to lightly bound nuclear matter. As the density is further increased the kink splits into a pair of half-kink constituents, providing a concrete realization of the previously suggested dyonic salt phase, where the bulk soliton splits into constituents at high density. The kink model also captures the phenomenon of baryonic popcorn, in which a first order phase transition generates an additional soliton layer in the holographic direction. We find that this popcorn transition takes place at a density below the dyonic salt phase, making the latter energetically unfavourable. However, the kink model predicts only one pop, rather than the sequence of pops suggested by previous approximations. In the kink model the two layers produced by the single pop form the surface of a soliton bag that increases in size as the baryon chemical potential is increased. The interior of the bag is filled with abelian electric potential and the instanton charge density is localized on the surface of the bag. The soliton bag may provide a holographic description of a quarkyonic phase.

How do stars affect ψDM halos?

NASA Astrophysics Data System (ADS)

Chan, James H. H.; Schive, Hsi-Yu; Woo, Tak-Pong; Chiueh, Tzihong

2018-04-01

Wave dark matter (ψDM) predicts a compact soliton core and a granular halo in every galaxy. This work presents the first simulation study of an elliptical galaxy by including both stars and ψDM, focusing on the systematic changes of the central soliton and halo granules. With the addition of stars in the inner halo, we find the soliton core consistently becomes more prominent by absorbing mass from the host halo than that without stars, and the halo granules become "non-isothermal", "hotter" in the inner halo and "cooler" in the outer halo, as opposed to the isothermal halo in pure ψDM cosmological simulations. Moreover, the composite (star+ψDM) mass density is found to follow a r-2 isothermal profile near the half-light radius in most cases. Most striking is the velocity dispersion of halo stars that increases rapidly toward the galactic center by a factor of at least 2 inside the half-light radius caused by the deepened soliton gravitational potential, a result that compares favorably with observations of elliptical galaxies and bulges in spiral galaxies. However in some rare situations we find a phase segregation turning a compact distribution of stars into two distinct populations with high and very low velocity dispersions; while the high-velocity component mostly resides in the halo, the very low-velocity component is bound to the interior of the soliton core, resembling stars in faint dwarf spheroidal galaxies.

Topology-induced bifurcations for the nonlinear Schrödinger equation on the tadpole graph.

PubMed

Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego

2015-01-01

In this paper we give the complete classification of solitons for a cubic nonlinear Schrödinger equation on the simplest network with a nontrivial topology: the tadpole graph, i.e., a ring with a half line attached to it and free boundary conditions at the junction. This is a step toward the modelization of condensate propagation and confinement in quasi-one-dimensional traps. The model, although simple, exhibits a surprisingly rich behavior and in particular we show that it admits: (i) a denumerable family of continuous branches of embedded solitons vanishing on the half line and bifurcating from linear eigenstates and threshold resonances of the system; (ii) a continuous branch of edge solitons bifurcating from the previous families at the threshold of the continuous spectrum with a pitchfork bifurcation; and (iii) a finite family of continuous branches of solitons without linear analog. All the solutions are explicitly constructed in terms of elliptic Jacobian functions. Moreover we show that families of nonlinear bound states of the above kind continue to exist in the presence of a uniform magnetic field orthogonal to the plane of the ring when a well definite flux quantization condition holds true. In this sense the magnetic field acts as a control parameter. Finally we highlight the role of resonances in the linearization as a signature of the occurrence of bifurcations of solitons from the continuous spectrum.

Different polarization dynamic states in a vector Yb-doped fiber laser.

PubMed

Li, Xingliang; Zhang, Shumin; Han, Huiyun; Han, Mengmeng; Zhang, Huaxing; Zhao, Luming; Wen, Fang; Yang, Zhenjun

2015-04-20

Different polarization dynamic states in an unidirectional, vector, Yb-doped fiber ring laser have been observed. A rich variety of dynamic states, including group velocity locked polarization domains and their splitting into regularly distributed multiple domains, polarization locked square pulses and their harmonic mode locking counterparts, and dissipative soliton resonances have all been observed with different operating parameters. We have also shown experimentally details of the conditions under which polarization-domain-wall dark pulses and bright square pulses form.

High Power Microwaves (HPM) (les Micro-ondes de forte puissance (MFP).

DTIC Science & Technology

1995-03-01

the polarization vector , [C/m 2], P1 is the polarization term which is linearly dependent on the electric field, and Pnl is The soliton laser [35...which utilizes Kerr nonlinearity in the polarization vector which is nonlinearly dependent on the optical fiber, has also been demonstrated. In the case...forward propa- then applied across the cathode. If the electric gating volume harmonics of the TMO1 mode, field is of the proper polarity , a phase tran- as

Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering

NASA Astrophysics Data System (ADS)

Maiden, M. D.; Bookman, L. D.; Hoefer, M. A.

2014-05-01

The interaction behaviors of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particle-like, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.

Characterizing traveling-wave collisions in granular chains starting from integrable limits: the case of the Korteweg-de Vries equation and the Toda lattice.

PubMed

Shen, Y; Kevrekidis, P G; Sen, S; Hoffman, A

2014-08-01

Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

Hopf solitons on compact manifolds

NASA Astrophysics Data System (ADS)

Ward, R. S.

2018-02-01

Hopf solitons in the Skyrme-Faddeev system on R3 typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the Skyrme term (the strong-coupling limit), then the picture simplifies. There is a topological lower bound E ≥ Q on the energy, and the local minima of E can look simple even for large Q. The aim here is to describe and investigate some of these solutions, when M is S3, T3, or S2 × S1. In addition, we review the more elementary baby-Skyrme system, with M being S2 or T2.

Multi-q crystal and magnetic structure in TbMnO3: Evidence for a Soliton-lattice

NASA Astrophysics Data System (ADS)

Aliouane, N.; Strempfer, J.; Caliebe, W.

2005-03-01

In TbMnO3, Mn-spins order with a sinusoidal antiferromagnetic (AF) propagation wave vector QMn=[0,k+/-q,l] (q˜0.288b^*) at TN(Mn)=41K. The propagation vector QMn varies with temperature on cooling until TLock(Mn) ˜30K, which coincides with a ferroelectric transition. In addition to QMn reflections we find magnetic reflections at 3QMn. Our X-ray measurements show that the magneto-elastic coupling gives rise to a structural modulation at twice the magnetic wavevector (2QMn). Field cooling the sample under a magnetic field oriented along the a-direction with H>9T shows that all magnetic wavevectors for Mn and Tb collapse to a single q structure with Q=[0,1/4,0], an up-up, down-down phase, and coincide with anomalies in the polarization. We argue that the temperature and field dependence of the magnetic and superlattice reflections are consistent with a soliton formalism which predicts a stable commensurate single q=1/4 phase [1]. [1] Kimura et al., PRB 68, 60403(2003).

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.

PubMed

Djoufack, Z I; Tala-Tebue, E; Nguenang, J P; Kenfack-Jiotsa, A

2016-10-01

We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.

Widely-pulsewidth-tunable ultrashort pulse generation from a birefringent carbon nanotube mode-locked fiber laser.

PubMed

Liu, Ya; Zhao, Xin; Liu, Jiansheng; Hu, Guoqing; Gong, Zheng; Zheng, Zheng

2014-08-25

We demonstrate the generation of soliton pulses covering a nearly one order-of-magnitude pulsewidth range from a simple carbon nanotube (CNT) mode-locked fiber laser with birefringence. A polarization-maintaining-fiber-pigtailed, inline polarization beam splitter and its associated birefringence is leveraged to either enable additional nonlinear polarization evolution (NPE) mode-locking effect or result in a bandwidth-tunable Lyot filter, through adjusting the intracavity polarization settings. The large pulsewidth tuning range is achieved by exploiting both the nonlinear CNT-NPE hybrid mode-locking mechanism that narrows the pulses and the linear filtering effect that broadens them. Induced vector soliton pulses with pulsewidth from 360 fs to 3 ps can be generated, and their time-bandwidth products indicate they are close to transform-limited.

Kepler unbound: Some elegant curiosities of classical mechanics

NASA Astrophysics Data System (ADS)

MacKay, Niall J.; Salour, Sam

2015-01-01

We explain two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger ("MICZ") Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of well-separated solitonic ("BPS") monopoles using Taub-NUT space. Each system is characterized by the conservation of a Laplace-Runge-Lenz vector, and we use elementary vector techniques to show that each obeys a subtly different variation on Kepler's three laws for the Newton-Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-09-01

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

Supersymmetrizing the Gorsky-Shifman-Yung soliton

NASA Astrophysics Data System (ADS)

Ireson, E.; Shifman, M.; Yung, A.

2018-05-01

We supersymmetrize the Hopfion studied by Gorsky et al. [Phys. Rev. D 88, 045026 (2013)., 10.1103/PhysRevD.88.045026]. This soliton represents a closed semilocal vortex string in U(1) gauge theory. It carries nonzero Hopf number due to the additional winding of a phase modulus as one moves along the closed string. We study this solution in N =2 supersymmetric QED with two flavors. As a preliminary exercise, we compactify one space dimension and consider a straight vortex with periodic boundary conditions. It turns out to be 1 /2 -BPS saturated. An additional winding along the string can be introduced and it does not spoil the BPS nature of the object. Next, we consider a ringlike vortex in a non-compact space and show that the circumference of the ring L can be stabilized once the previously mentioned winding along the string is introduced. Of course, the ringlike vortex is not BPS but its energy becomes close to the BPS bound if L is large, which can be guaranteed in the case that we have a large value of the angular momentum J . Thus we arrive at the concept of asymptotically BPS-saturated solitons. BPS saturation is achieved in the limit J →∞ .

Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges

NASA Astrophysics Data System (ADS)

Blas, Harold; Callisaya, Hector Flores

2018-02-01

We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities, split into two infinite towers of conserved and asymptotically conserved charges. For two-solitons without definite parity under space-reflection symmetry (kink-kink and kink-antikink scatterings with unequal and opposite velocities) our numerical results show the existence of the asymptotically conserved charges only. However, we show that in the center-of-mass reference frame of the two solitons the parity symmetries and their associated set of exactly conserved charges can be restored. Moreover, the positive parity breather-like (kink-antikink bound state) solution exhibits a tower of exactly conserved charges and a subset of charges which are periodic in time. We back up our results with extensive numerical simulations which also demonstrate the existence of long lived breather-like states in these models. The time evolution has been simulated by the 4th order Runge-Kutta method supplied with non-reflecting boundary conditions.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Noise-like pulse trapping in a figure-eight fiber laser.

PubMed

Luo, Ai-Ping; Luo, Zhi-Chao; Liu, Hao; Zheng, Xu-Wu; Ning, Qiu-Yi; Zhao, Nian; Chen, Wei-Cheng; Xu, Wen-Cheng

2015-04-20

We report on the trapping of noise-like pulse in a figure-eight fiber laser mode locked by nonlinear amplifier loop mirror (NALM). After achievement of noise-like vector pulse, it was found that the wavelength shift of the two resolved polarization components responsible for the pulse trapping was very sensitive to the cavity birefringence. By properly rotating the polarization controllers (PCs), the wavelength shift could be up to 4.8 nm, which is much larger than that of conventional soliton trapping. The observed results would shed some light on the fundamental physics of noise-like pulse as well as its vector features in fiber lasers.

Coping with the Bounds: Speculations on Nonlinearity in Military Affairs

DTIC Science & Technology

2003-08-01

organizing criticality, cellular automata, solitons, and so on–because they all globally share this property . Nonlinearity reflects the science of the...Why does it matter? One rea- son for emphasizing nonlinearity is that it constitutes the well-established mathematical property underlying and making...have some hints as to what those principles might be.3 Complex adaptive systems, or cas, contain seven basic attributes. These consist of four properties

USSR Report, Physics and Mathematics

DTIC Science & Technology

1984-05-07

E- vector of the incident wave and the grating lines. The polarizer and analyzer were two MLR-1 germanium plates oriented at the Brewster angle...with active mode locking is available as a source of radiation in the X = 3 ;um band for generating infrared solitons . Figures 2, references 15: 7...Bol’shakov, et al.; ZHURNAL PRIKLADNOY SPEKTROSKOPII, No 5, Nov 83) 19 Experimental Study of Polarization Characteristics of Reflective Diffraction

Optical solitons in nematic liquid crystals: model with saturation effects

NASA Astrophysics Data System (ADS)

Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego; de la Vega, Constanza Sánchez F.

2018-04-01

We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.

1-norm support vector novelty detection and its sparseness.

PubMed

Zhang, Li; Zhou, WeiDa

2013-12-01

This paper proposes a 1-norm support vector novelty detection (SVND) method and discusses its sparseness. 1-norm SVND is formulated as a linear programming problem and uses two techniques for inducing sparseness, or the 1-norm regularization and the hinge loss function. We also find two upper bounds on the sparseness of 1-norm SVND, or exact support vector (ESV) and kernel Gram matrix rank bounds. The ESV bound indicates that 1-norm SVND has a sparser representation model than SVND. The kernel Gram matrix rank bound can loosely estimate the sparseness of 1-norm SVND. Experimental results show that 1-norm SVND is feasible and effective. Copyright © 2013 Elsevier Ltd. All rights reserved.

Stability of the lepton bag model based on the Kerr–Newman solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burinskii, A., E-mail: bur@ibrae.ac.ru

2015-11-15

We show that the lepton bag model considered in our previous paper [10], generating the external gravitational and electromagnetic fields of the Kerr–Newman (KN) solution, is supersymmetric and represents a BPS-saturated soliton interpolating between the internal vacuum state and the external KN solution. We obtain Bogomolnyi equations for this phase transition and show that the Bogomolnyi bound determines all important features of this bag model, including its stable shape. In particular, for the stationary KN solution, the BPS bound provides stability of the ellipsoidal form of the bag and the formation of the ring–string structure at its border, while formore » the periodic electromagnetic excitations of the KN solution, the BPS bound controls the deformation of the surface of the bag, reproducing the known flexibility of bag models.« less

Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong

2017-04-01

We investigate the defocusing coupled nonlinear Schrödinger equations from a 3×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.

Understanding the core-halo relation of quantum wave dark matter from 3D simulations.

PubMed

Schive, Hsi-Yu; Liao, Ming-Hsuan; Woo, Tak-Pong; Wong, Shing-Kwong; Chiueh, Tzihong; Broadhurst, Tom; Hwang, W-Y Pauchy

2014-12-31

We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter, described by the Schrödinger-Poisson (SP) equation with a particle mass ∼10(-22)  eV. A distinct gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark matter scenarios. Furthermore, we show that each solitonic core is surrounded by an extended halo composed of large fluctuating dark matter granules which modulate the halo density on a scale comparable to the diameter of the solitonic core. The scaling symmetry of the SP equation and the uncertainty principle tightly relate the core mass to the halo specific energy, which, in the context of cosmological structure formation, leads to a simple scaling between core mass (Mc) and halo mass (Mh), Mc∝a(-1/2)Mh(1/3), where a is the cosmic scale factor. We verify this scaling relation by (i) examining the internal structure of a statistical sample of virialized halos that form in our 3D cosmological simulations and by (ii) merging multiple solitons to create individual virialized objects. Sufficient simulation resolution is achieved by adaptive mesh refinement and graphic processing units acceleration. From this scaling relation, present dwarf satellite galaxies are predicted to have kiloparsec-sized cores and a minimum mass of ∼10(8)M⊙, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of 2×10(12)M⊙ at z=8 should have massive solitonic cores of ∼2×10(9)M⊙ within ∼60  pc. Such cores can provide a favorable local environment for funneling the gas that leads to the prompt formation of early stellar spheroids and quasars.

Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential.

PubMed

Xu, Si-Liu; Zhao, Guo-Peng; Belić, Milivoj R; He, Jun-Rong; Xue, Li

2017-04-17

We analyze three-dimensional (3D) vector solitary waves in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity, under action of a composite self-consistent trapping potential. Exact vector solitary waves, or light bullets (LBs), are found using the self-similarity method. The stability of vortex 3D LB pairs is examined by direct numerical simulations; the results show that only low-order vortex soliton pairs with the mode parameter values n ≤ 1, l ≤ 1 and m = 0 can be supported by the spatially modulated interaction in the composite trap. Higher-order LBs are found unstable over prolonged distances.

JPRS Report, Science & Technology. USSR: Physics & Mathematics

DTIC Science & Technology

1987-10-29

Pulse Holography (S. D. Nikolayev, I. 0. Starobogatov; OPTIKA I SPEKTROSKOPIYA, No 5, Nov 86) 22 NUCLEAR PHYSICS Masses of Vector and Quasi-Scalar...86) 32 Anomalous Evolution of Optical Solitons (S. 0. Yelyutin, A. I. Maymistov; OPTIKA I SPEKTROSKOPIYA, No 5, Nov 86) • ."’. 33 Four-Level...of Polarization Modes in Birefringent Single-Mode Fiber-Optic Waveguide (F. A. Shatalov; OPTIKA I SPEKTROSKOPIYA, No 2, Feb 87)..’.. 3U High

JPRS Report. Science & Technology: China.

DTIC Science & Technology

1989-03-17

From Simple Colliding-Pulse Mode- Locking Dye Laser With Double Coated Stack Mirrors [Wang Qingyue, et al.; GUANGXUE XUEBAO, No 11, Nov 88] 82...86 Influence of Stimulated Raman Process on Fundamental Solitons in Fibers [Qu Linjie, et al.; GUANGXUE XUEBAO, No 11, Nov 88] 87 650 nm...synapses are the same regarding the relationship of he and hi to N. Each component of the vector lat represents the delay time lat of each synapse as it

Code Samples Used for Complexity and Control

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Ultralight Axion Dark Matter and Its Impact on Dark Halo Structure in N-body Simulations

NASA Astrophysics Data System (ADS)

Zhang, Jiajun; Sming Tsai, Yue-Lin; Kuo, Jui-Lin; Cheung, Kingman; Chu, Ming-Chung

2018-01-01

Ultralight axion is a dark matter candidate with mass { O }({10}-22){eV} and de Broglie wavelength of order kiloparsec. Such an axion, also called fuzzy dark matter (FDM), thermalizes via gravitational force and forms a Bose–Einstein condensate. Recent studies suggested that the quantum pressure from FDM can significantly affect structure formation in small scales, thus alleviating the so-called “small-scale crisis.” In this paper, we develop a new technique to discretize the quantum pressure and illustrate the interactions among FDM particles in an N-body simulation that accurately simulates the formation of the dark matter halo and its inner structure in the region outside the softening length. In a self-gravitationally bound virialized halo, we find a constant density solitonic core, which is consistent with theoretical prediction. The existence of the solitonic core reveals the nonlinear effect of quantum pressure and impacts structure formation in the FDM model.

Parametric excitation of multiple resonant radiations from localized wavepackets

PubMed Central

Conforti, Matteo; Trillo, Stefano; Mussot, Arnaud; Kudlinski, Alexandre

2015-01-01

Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A remarkable property of such driving is that it can induce the localized (bound) states to resonantly couple to the continuum. Therefore experiments that allow for enlightening and controlling the mechanisms underlying such coupling are of paramount importance. We implement such an experiment in a special optical fiber characterized by a dispersion oscillating along the propagation coordinate, which mimics “time”. The quasi-momentum associated with such periodic perturbation is responsible for the efficient coupling of energy from the localized wave-packets (solitons in anomalous dispersion and shock fronts in normal dispersion) sustained by the fiber nonlinearity, into free-running linear dispersive waves (continuum) at multiple resonant frequencies. Remarkably, the observed resonances can be explained by means of a unified approach, regardless of the fact that the localized state is a soliton-like pulse or a shock front. PMID:25801054

Ground state of high-density matter

NASA Technical Reports Server (NTRS)

Copeland, ED; Kolb, Edward W.; Lee, Kimyeong

1988-01-01

It is shown that if an upper bound to the false vacuum energy of the electroweak Higgs potential is satisfied, the true ground state of high-density matter is not nuclear matter, or even strange-quark matter, but rather a non-topological soliton where the electroweak symmetry is exact and the fermions are massless. This possibility is examined in the standard SU(3) sub C tensor product SU(2) sub L tensor product U(1) sub Y model. The bound to the false vacuum energy is satisfied only for a narrow range of the Higgs boson masses in the minimal electroweak model (within about 10 eV of its minimum allowed value of 6.6 GeV) and a somewhat wider range for electroweak models with a non-minimal Higgs sector.

Optical Solitons

NASA Astrophysics Data System (ADS)

Taylor, J. R.

2005-08-01

1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.

Optical Solitons

NASA Astrophysics Data System (ADS)

Taylor, J. R.

1992-04-01

1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.

Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit.

PubMed

Cai, Xin; Liu, Jinsong; Wang, Shenglie

2009-02-16

This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2017-02-01

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky-Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.

Soliton Turbulence in Shallow Water Ocean Surface Waves

NASA Astrophysics Data System (ADS)

Costa, Andrea; Osborne, Alfred R.; Resio, Donald T.; Alessio, Silvia; Chrivı, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E.

2014-09-01

We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ˜ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ˜ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.

Model-Independent Bounds on Kinetic Mixing

DOE PAGES

Hook, Anson; Izaguirre, Eder; Wacker, Jay G.

2011-01-01

New Abelimore » an vector bosons can kinetically mix with the hypercharge gauge boson of the Standard Model. This letter computes the model-independent limits on vector bosons with masses from 1 GeV to 1 TeV. The limits arise from the numerous e + e − experiments that have been performed in this energy range and bound the kinetic mixing by ϵ ≲ 0.03 for most of the mass range studied, regardless of any additional interactions that the new vector boson may have.« less

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com; Mahalingam, A.; Uthayakumar, A.

We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons,more » study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.« less

Optical spatial solitons: historical overview and recent advances.

PubMed

Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N

2012-08-01

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Stokes solitons in optical microcavities

NASA Astrophysics Data System (ADS)

Yang, Qi-Fan; Yi, Xu; Yang, Ki Youl; Vahala, Kerry

2017-01-01

Solitons are wave packets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fibre waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers, and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities, thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics, including nonlinear optics and spectroscopy.

Coupling effects for separate spatial solitons in a biased series centrosymmetric photorefractive crystal circuit considering grey solitons

NASA Astrophysics Data System (ADS)

Katti, Aavishkar; Yadav, Ram Anjore

2018-02-01

The existence and coupling of grey-grey, grey-bright and grey-dark separate spatial solitons in a biased series centrosymmetric photorefractive crystal circuit is investigated for the first time. The numerical solution of the separate spatial solitons is presented. The coupling between the two separate spatial solitons is analysed for all three cases of separate coupled solitons, namely grey-grey, grey-bright, and grey-dark. Changing the intensity of the soliton in one crystal affects the soliton in both crystals due to flow of the light induced current through the circuit. The effect of the background intensity of each crystal on both the spatial solitons is investigated. Also, the effect of changing the temperature of one crystal affects the soliton in both crystals due to the coupling effect. The soliton width dependence on the temperature is different for each crystal.

Theory of the Motion of Ball Lightning

NASA Astrophysics Data System (ADS)

Handel, Peter

2008-04-01

The Maser-Soliton Theory of BL predicts the dynamics of each of the harmonic waves in the wave packet that feeds and in fact defines the Langmuir plasma soliton that is observed as BL. The frequencies in the wave packet are in a narrow window f that corresponds in the case of open air BL to the diameter of the area in which the damage caused by the final explosion of the BL is observed. This is usually of the order of δx=30 m roughly, in rms. The corresponding wave vector interval is δk=(1/2)(1/30m)=0.017/m in rms. At the same time, k is of the order of 6/m, yielding k/δk=360. This pronounced line-narrowing is obtained due to the large gain of the atmospheric maser when it generates the Kapitsa standing wave. Phase differences between the waves that make up the electromagnetic field that couples with the electrostatic field of the soliton are determined by the frequency dependence of gain and dissipation. They are influenced less by the motion of the air, than by the maser dynamics and by the boundary conditions shaping the electromagnetic field, i.e. the individual photonic wave-packet. The paper presents the equations that determine the phase dynamics and therefore also the observed motion of BL. A similar phase dynamics is expected to be applicable to the special case of UFO motions.

Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit.

PubMed

Liu, Jinsong; Hao, Zhonghua

2002-06-01

This paper presents calculations for an idea in photorefractive spatial soliton, namely, screening solitons form in a biased series photorefractive crystal circuit consisting of two photorefractive crystals connected electronically by electrode leads in a chain with a voltage source. A system of two coupled equations is derived under appropriate conditions for two-beam propagation in the crystal circuit. The possibility of obtaining steady-state bright and dark screening soliton solutions is investigated in one dimension and, the existence of dark-dark, bright-dark, and bright-bright separate screening soliton pairs in such a circuit is proved. The numerical results show that the two solitons in a soliton pair can affect each other by the light-induced current and their coupling can affect their spatial profiles, dynamical evolutions, stabilities, and self-deflection. Under the limit in which the optical wave has a spatial extent much less than the width of the crystal, only the dark soliton can affect the other soliton by the light-induced current, but the bright soliton cannot. For a bright-dark or dark-dark soliton pair, the dark soliton in a weak input intensity can be obtained for a larger nonlinearity than for a stronger input intensity. For a bright-dark soliton pair, increasing the input intensity of the dark soliton can increase the bending angle of the bright soliton. Some potential applications are discussed.

Nonlinear High-Energy Pulse Propagation in Graded-Index Multimode Optical Fibers for Mode-Locked Fiber Lasers

DTIC Science & Technology

2014-12-23

coupled for d = 2λ . Results are shown for the TE polarization , where the transverse electric field vector is pointing in the vertical direction in these...16, 42–44 (1991). 6. D. U. Noske, N. Pandit, and J. R. Taylor, “Subpicosecond soliton pulse formation from self-mode- locked erbium fibre laser using...High-Energy Pulse Propagation in Graded-Index Multimode Optical Fibers for Mode- Locked Fiber Lasers 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1

Waveguide coupling in the few-cycle regime

NASA Astrophysics Data System (ADS)

Leblond, Hervé; Terniche, Said

2016-04-01

We consider the coupling of two optical waveguides in the few-cycle regime. The analysis is performed in the frame of a generalized Kadomtsev-Petviashvili model. A set of two coupled modified Korteweg-de Vries equations is derived, and it is shown that three types of coupling can occur, involving the linear index, the dispersion, or the nonlinearity. The linear nondispersive coupling is investigated numerically, showing the formation of vector solitons. Separate pulses may be trapped together if they have not initially the same location, size, or phase, and even if their initial frequencies differ.

Distinguishing boson stars from black holes and neutron stars from tidal interactions in inspiraling binary systems

NASA Astrophysics Data System (ADS)

Sennett, Noah; Hinderer, Tanja; Steinhoff, Jan; Buonanno, Alessandra; Ossokine, Serguei

2017-07-01

Binary systems containing boson stars—self-gravitating configurations of a complex scalar field—can potentially mimic black holes or neutron stars as gravitational-wave sources. We investigate the extent to which tidal effects in the gravitational-wave signal can be used to discriminate between these standard sources and boson stars. We consider spherically symmetric boson stars within two classes of scalar self-interactions: an effective-field-theoretically motivated quartic potential and a solitonic potential constructed to produce very compact stars. We compute the tidal deformability parameter characterizing the dominant tidal imprint in the gravitational-wave signals for a large span of the parameter space of each boson star model, covering the entire space in the quartic case, and an extensive portion of interest in the solitonic case. We find that the tidal deformability for boson stars with a quartic self-interaction is bounded below by Λmin≈280 and for those with a solitonic interaction by Λmin≈1.3 . We summarize our results as ready-to-use fits for practical applications. Employing a Fisher matrix analysis, we estimate the precision with which Advanced LIGO and third-generation detectors can measure these tidal parameters using the inspiral portion of the signal. We discuss a novel strategy to improve the distinguishability between black holes/neutrons stars and boson stars by combining tidal deformability measurements of each compact object in a binary system, thereby eliminating the scaling ambiguities in each boson star model. Our analysis shows that current-generation detectors can potentially distinguish boson stars with quartic potentials from black holes, as well as from neutron-star binaries if they have either a large total mass or a large (asymmetric) mass ratio. Discriminating solitonic boson stars from black holes using only tidal effects during the inspiral will be difficult with Advanced LIGO, but third-generation detectors should be able to distinguish between binary black holes and these binary boson stars.

Highly stable families of soliton molecules in fiber-optic systems

NASA Astrophysics Data System (ADS)

Moubissi, A.-B.; Tchofo Dinda, P.; Nse Biyoghe, S.

2018-04-01

We develop an efficient approach to the design of families of single solitons and soliton molecules most suited to a given fiber system. The obtained solitonic entities exhibit very high stability, with a robustness which allows them to propagate over thousands of kilometers and to survive collisions with other solitonic entities. Our approach enables the generation of a large number of solitonic entities, including families of single solitons and two-soliton molecules, which can be distinguished sufficiently by their respective profiles or energy levels, and so can be easily identifiable and detectable without ambiguity. We discuss the possible use of such solitonic entities as symbols of a multi-level modulation format in fiber-optic communication systems.

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

PubMed

Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A

2016-08-01

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.

Cylindrical fast magnetosonic solitary waves in quantum degenerate electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Abdikian, A.

2018-02-01

The nonlinear properties of fast magnetosonic solitary waves in a quantum degenerate electron-positron (e-p) plasma in the presence of stationary ions for neutralizing the plasma background of bounded cylindrical geometry were studied. By employing the standard reductive perturbation technique and the quantum hydrodynamic model for the e-p fluid, the cylindrical Kadomtsev-Petviashvili (CKP) equation was derived for small, but finite, amplitude waves and was given the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars. By a suitable coordinate transformation, the CKP equation can be solved analytically. An analytical solution for magnetosonic solitons and periodic waves is presented. The numerical results reveal that the Bohm potential has a main effect on the periodic and solitary wave structures. By increasing the values of the plasma parameters, the amplitude of the solitary wave will be increased. The present study may be helpful in the understanding of nonlinear electromagnetic soliton waves propagating in both laboratory and astrophysical plasmas, and can help in providing good agreement between theoretical results and laboratory plasma experiments.

Hydrodynamic optical soliton tunneling

NASA Astrophysics Data System (ADS)

Sprenger, P.; Hoefer, M. A.; El, G. A.

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Hydrodynamic optical soliton tunneling.

PubMed

Sprenger, P; Hoefer, M A; El, G A

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Dark and antidark solitons in the modified nonlinear Schrödinger equation accounting for the self-steepening effect.

PubMed

Li, Min; Tian, Bo; Liu, Wen-Jun; Zhang, Hai-Qiang; Wang, Pan

2010-04-01

In this paper, the modified nonlinear Schrödinger equation is investigated, which describes the femtosecond optical pulse propagation in a monomodal optical fiber. Based on the Wadati-Konno-Ichikawa system, another type of Lax pair and infinitely many conservation laws are derived. Dark and antidark soliton solutions in the normal dispersion regime are obtained by means of the Hirota method. Parametric regions for the existence of the dark and antidark soliton solutions are given. Asymptotic analysis of the two-soliton solution shows that collisions between two solitons (two antidark solitons, two dark solitons, and dark and antidark solitons) are elastic. In addition, collision between dark and antidark solitons reveals that dark and antidark solitons can co-exist on the same background in the normal dispersion regime.

Dark-soliton collisions for a coupled AB system in the geophysical fluids or nonlinear optics

NASA Astrophysics Data System (ADS)

Xie, Xi-Yang; Meng, Gao-Qing

2018-02-01

Under investigation in this paper is a coupled AB system, which describes the marginally unstable baroclinic wave packets in the geophysical fluids or ultra-short pulses in nonlinear optics. As the dark solitons are more resistant against various perturbations than the bright ones, we aim to investigate the dark solitons in the geophysical fluids or nonlinear optics. Dark one- and two-soliton solutions for such a system are derived based on the bilinear forms and propagations of the one solitons and collisions between the two solitons are graphically illustrated and analyzed. Further, influences of the coefficients λ and σ on the solitons are discussed, where λ is a parameter measuring the state of the basic flow and σ is the group velocity. The dark-one solitons with invariant shapes and amplitudes are viewed, and elastic collisions between the dark-two solitons are observed. Also, elastic collision between the bright and dark solitons is viewed, and the dark soliton is found to possess two peaks. σ is found to affect the widths of the dark-one solitons and the travelling directions of the dark-two solitons. It is shown that λ cannot influence shapes of A1 and A2, but affect the plane of the one soliton for B, and the two-peak dark soliton for B changes to the single-peak one with the value of λ decreasing, where A1 and A2 are the packets of short waves and B is the mean flow.

Modeling of mode-locked fiber lasers

NASA Astrophysics Data System (ADS)

Shaulov, Gary

This thesis presents the results of analytical and numerical simulations of mode-locked fiber lasers and their components: multiple quantum well saturable absorbers and nonlinear optical loop mirrors. Due to the growing interest in fiber lasers as a compact source of ultrashort pulses there is a need to develop a full understanding of the advantages and limitations of the different mode-locked techniques. The mode-locked fiber laser study performed in this thesis can be used to optimize the design and performance of mode-locked fiber laser systems. A group at Air Force Research Laboratory reported a fiber laser mode-locked by multiple quantum well (MQW) saturable absorber with stable pulses generated as short as 2 ps [21]. The laser cavity incorporates a chirped fiber Bragg grating as a dispersion element; our analysis showed that the laser operates in the soliton regime. Soliton perturbation theory was applied and conditions for stable pulse operation were investigated. Properties of MQW saturable absorbers and their effect on cavity dynamics were studied and the cases of fast and slow saturable absorbers were considered. Analytical and numerical results are in a good agreement with experimental data. In the case of the laser cavity with a regular fiber Bragg grating, the properties of MQW saturable absorbers dominate the cavity dynamics. It was shown that despite the lack of a soliton shaping mechanism, there is a regime in parameter space where stable or quasi-stable solitary waves solutions can exist. Further a novel technique of fiber laser mode-locking by nonlinear polarization rotation was proposed. Polarization rotation of vector solitons was simulated in a birefringent nonlinear optical loop mirror (NOLM) and the switching characteristics of this device was studied. It was shown that saturable absorber-like action of NOLM allows mode-locked operation of the two fiber laser designs. Laser cavity designs were proposed: figure-eight-type and sigma-type cavity.

Steady bound electromagnetic eigenstate arises in a homogeneous isotropic linear metamaterial with zero-real-part-of-impedance and nonzero-imaginary-part-of-wave-vector

NASA Astrophysics Data System (ADS)

Chen, Jiangwei; Dai, Yuyao; Yan, Lin; Zhao, Huimin

2018-04-01

In this paper, we shall demonstrate theoretically that steady bound electromagnetic eigenstate can arise in an infinite homogeneous isotropic linear metamaterial with zero-real-part-of-impedance and nonzero-imaginary-part-of-wave-vector, which is partly attributed to that, here, nonzero-imaginary-part-of-wave-vector is not involved with energy losses or gain. Altering value of real-part-of-impedance of the metamaterial, the bound electromagnetic eigenstate may become to be a progressive wave. Our work may be useful to further understand energy conversion and conservation properties of electromagnetic wave in the dispersive and absorptive medium and provides a feasible route to stop, store and release electromagnetic wave (light) conveniently by using metamaterial with near-zero-real-part-of-impedance.

Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation

NASA Astrophysics Data System (ADS)

Zhang, Xiaoen; Chen, Yong

2017-11-01

In this paper, a combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo-Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission. Particularly, a new combination of positive quadratic functions and hyperbolic functions is considered, and then a novel nonlinear phenomenon is explored. Via this method, a pair of resonance kink stripe solitons and rogue wave is studied. Rogue wave is triggered by the interaction between lump soliton and a pair of resonance kink stripe solitons. It is exciting that rogue wave must be attached to the stripe solitons from its appearing to disappearing. The whole progress is completely symmetry, the rogue wave starts itself from one stripe soliton and lose itself in another stripe soliton. The dynamic properties of the interaction between one stripe soliton and lump soliton, rogue wave are discussed by choosing appropriate parameters.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sazonov, S. V., E-mail: sazonov.sergey@gmail.com; Ustinov, N. V., E-mail: n-ustinov@mail.ru

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutionsmore » of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.« less

Neutron Electric Dipole Moment from Gauge-String Duality.

PubMed

Bartolini, Lorenzo; Bigazzi, Francesco; Bolognesi, Stefano; Cotrone, Aldo L; Manenti, Andrea

2017-03-03

We compute the electric dipole moment of nucleons in the large N_{c} QCD model by Witten, Sakai, and Sugimoto with N_{f}=2 degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological θ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result-a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be d_{n}=1.8×10^{-16}θ e cm. The electric dipole moment of the proton is exactly the opposite.

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions. A review and a perspective

NASA Astrophysics Data System (ADS)

Cartes, C.; Descalzi, O.; Brand, H. R.

2014-10-01

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems. It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.

Observation of surface dark photovoltaic solitons.

PubMed

Yang, Xi; Chen, Weiqiang; Yao, Peng; Zhang, Tianhao; Tian, Jianguo; Xu, Jingjun

2013-02-25

Surface dark solitons in photovoltaic nonlinear media are reported. Taking advantage of diffusion and photovoltaic nonlinearities we demonstrated the surface dark solitons and their behaviors near surface theoretically and experimentally in LiNbO₃ crystal. It is very interesting that surface dark soliton is just half of dark soliton in bulk. Another interesting thing is that transverse modulation instability can be perfectly suppressed by surface dark soliton in virtue of surface. In addition, surface waveguides were written successfully utilizing surface dark soliton.

Relation between nonlocal surface and bulk dark solitons

NASA Astrophysics Data System (ADS)

Gao, Xinghui; Zhang, Chengyun; Wang, Qing

2018-06-01

We investigate the existence and stability of nonlocal surface dark solitons at the interface formed by a nonlocal nonlinear self-defocusing medium and a linear medium. We find that nonlocal fundamental surface dark solitons are always stable in their entire existence domain, while high-order surface dark solitons are oscillatory stable. Comparing with nonlocal bulk dark solitons in amplitude and boundary conditions, nonlocal surface dark solitons can be regarded as the half of the corresponding bulk dark solitons with antisymmetrical amplitude distribution.

Brownian motion of solitons in a Bose-Einstein condensate.

PubMed

Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B

2017-03-07

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

Line soliton interactions of the Kadomtsev-Petviashvili equation.

PubMed

Biondini, Gino

2007-08-10

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line solitons as y-->-infinity. We also show that the (2N-1)!! types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.

Generation of straight-line shifting bright-dark soliton trains with a wide dip in the symmetric center or dark solitons in optical fibers

NASA Astrophysics Data System (ADS)

Zhong, Xianqiong; Yao, Na; Sheng, Jia'nan; Cheng, Ke

2018-02-01

Nonlinear evolutions of dark soliton pulses with initially constant frequency chirps are investigated numerically for different soliton orders and chirp parameters in different dispersion regimes of optical fibers. The results show interestingly that, in the normal dispersion regime, the evolution properties remain unchanged apart from their straight-line shifts of the temporal trajectories compared with the chirp-free case. While in the anomalous dispersion regime, the dark solitons can evolve to bright-dark soliton trains with a wide black soliton in the symmetric center. The longer the distance, the more the pulse number. The larger the soliton order, the more the pulse number at the same distance. Similarly, straight-line shift of the temporal trajectory of the bright-dark soliton trains will also appear. The shifting amount and direction depend on the absolute value and the sign of the chirp parameter, respectively. This result inspires people to generate bright-dark soliton trains by using ordinary passive optical fibers instead of fiber lasers. Besides, this work also provides us an alternative approach to guide the formed solitons or soliton trains to move their temporal trajectories along straight lines.

Initial conditions for dark soliton generation in normal-dispersion fiber lasers.

PubMed

Ge, Y Q; Luo, J L; Li, L; Jin, X X; Tang, D Y; Shen, D Y; Zhang, S M; Zhao, L M

2015-01-01

We report results of numerical simulations on the various initial conditions for dark soliton generation in an all-normal-dispersion fiber laser. All the dark solitons generated are odd dark solitons. Differently from the dark soliton generation in fibers, where an arbitrary dip could evolve into a dark soliton, it is found that the dark soliton can originate only from an initial dip with a certain parameter requirement. A bright pulse with either a hyperbolic secant square, Gaussian, or Lorentz profile can be developed into a dark soliton, provided that the parameters of the initial bright pulse are selected. Dark solitons can be generated in fiber lasers only if there is a phase jump, and this phase jump can be maintained and evolve to π during the pulse evolution.

Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework.

PubMed

Slunyaev, A V; Pelinovsky, E N

2016-11-18

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.

Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework

NASA Astrophysics Data System (ADS)

Slunyaev, A. V.; Pelinovsky, E. N.

2016-11-01

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.

Quadratic spatial soliton interactions

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.

Black hole superradiance signatures of ultralight vectors

NASA Astrophysics Data System (ADS)

Baryakhtar, Masha; Lasenby, Robert; Teo, Mae

2017-08-01

The process of superradiance can extract angular momentum and energy from astrophysical black holes (BHs) to populate gravitationally bound states with an exponentially large number of light bosons. We analytically calculate superradiant growth rates for vectors around rotating BHs in the regime where the vector Compton wavelength is much larger than the BH size. Spin-1 bound states have superradiance times as short as a second around stellar BHs, growing up to a thousand times faster than their spin-0 counterparts. The fast rates allow us to use measurements of rapidly spinning BHs in x-ray binaries to exclude a wide range of masses for weakly coupled spin-1 particles, 5 ×10-14-2 ×10-11 eV ; lighter masses in the range 6 ×10-20-2 ×10-17 eV start to be constrained by supermassive BH spin measurements at a lower level of confidence. We also explore routes to detection of new vector particles possible with the advent of gravitational wave (GW) astronomy. The LIGO-Virgo Collaboration could discover hints of a new light vector particle in statistical analyses of masses and spins of merging BHs. Vector annihilations source continuous monochromatic gravitational radiation which could be observed by current GW observatories. At design sensitivity, Advanced LIGO may measure up to thousands of annihilation signals from within the Milky Way, while hundreds of BHs born in binary mergers across the observable Universe may superradiate vector bound states and become new beacons of monochromatic gravitational waves.

Dark solitons with Majorana fermions in spin-orbit-coupled Fermi gases.

PubMed

Xu, Yong; Mao, Li; Wu, Biao; Zhang, Chuanwei

2014-09-26

We show that a single dark soliton can exist in a spin-orbit-coupled Fermi gas with a high spin imbalance, where spin-orbit coupling favors uniform superfluids over nonuniform Fulde-Ferrell-Larkin-Ovchinnikov states, leading to dark soliton excitations in highly imbalanced gases. Above a critical spin imbalance, two topological Majorana fermions without interactions can coexist inside a dark soliton, paving a way for manipulating Majorana fermions through controlling solitons. At the topological transition point, the atom density contrast across the soliton suddenly vanishes, suggesting a signature for identifying topological solitons.

Generation of dark solitons and their instability dynamics in two-dimensional condensates

NASA Astrophysics Data System (ADS)

Verma, Gunjan; Rapol, Umakant D.; Nath, Rejish

2017-04-01

We analyze numerically the formation and the subsequent dynamics of two-dimensional matter wave dark solitons in a Thomas-Fermi rubidium condensate using various techniques. An initially imprinted sharp phase gradient leads to the dynamical formation of a stationary soliton as well as very shallow gray solitons, whereas a smooth gradient only creates gray solitons. The depth and hence, the velocity of the soliton is provided by the spatial width of the phase gradient, and it also strongly influences the snake-instability dynamics of the two-dimensional solitons. The vortex dipoles stemming from the unstable soliton exhibit rich dynamics. Notably, the annihilation of a vortex dipole via a transient dark lump or a vortexonium state, the exchange of vortices between either a pair of vortex dipoles or a vortex dipole and a single vortex, and so on. For sufficiently large width of the initial phase gradient, the solitons may decay directly into vortexoniums instead of vortex pairs, and also the decay rate is augmented. Later, we discuss alternative techniques to generate dark solitons, which involve a Gaussian potential barrier and time-dependent interactions, both linear and periodic. The properties of the solitons can be controlled by tuning the amplitude or the width of the potential barrier. In the linear case, the number of solitons and their depths are determined by the quench time of the interactions. For the periodic modulation, a transient soliton lattice emerges with its periodicity depending on the modulation frequency, through a wave number selection governed by the local Bogoliubov spectrum. Interestingly, for sufficiently low barrier potential, both Faraday pattern and soliton lattice coexist. The snake instability dynamics of the soliton lattice is characteristically modified if the Faraday pattern is present.

Dark soliton dynamics and interactions in continuous-wave-induced lattices.

PubMed

Tsopelas, Ilias; Kominis, Yannis; Hizanidis, Kyriakos

2007-10-01

The dynamics of dark spatial soliton beams and their interaction under the presence of a continuous wave (CW), which dynamically induces a photonic lattice, are investigated. It is shown that appropriate selection of the characteristic parameters of the CW result in controllable steering of a single soliton as well as controllable interaction between two solitons. Depending on the CW parameters, the soliton angle of propagation can be changed drastically, while two-soliton interaction can be either enhanced or reduced, suggesting a reconfigurable soliton control mechanism. Our analytical approach, based on the variational perturbation method, provides a dynamical system for the dark soliton evolution parameters. Analytical results are shown in good agreement with direct numerical simulations.

A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves.

PubMed

Declercq, Nico F; Leroy, Oswald

2011-08-01

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing. Copyright © 2011. Published by Elsevier B.V.

Ponderable soliton stars

NASA Technical Reports Server (NTRS)

Chiu, Hong-Yee

1990-01-01

The theory of Lee and Pang (1987), who obtained solutions for soliton stars composed of zero-temperature fermions and bosons, is applied here to quark soliton stars. Model soliton stars based on a simple physical model of the proton are computed, and the properties of the solitons are discussed, including the important problem of the existence of a limiting mass and thus the possible formation of black holes of primordial origin. It is shown that there is a definite mass limit for ponderable soliton stars, so that during cooling a soliton star might reach a stage beyond which no equilibrium configuration exists and the soliton star probably will collapse to become a black hole. The radiation of ponderable soliton stars may alter the short-wavelength character of the cosmic background radiation, and may be observed as highly redshifted objects at z of about 100,000.

Multi-dimensional stable fundamental solitons and excitations in PT-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions

NASA Astrophysics Data System (ADS)

Chen, Yong; Yan, Zhenya

2018-04-01

We demonstrate the parity-time- (PT-) symmetric harmonic-Gaussian potential with unbounded gain-and-loss distribution can support entirely-real linear spectra, stable spatial and spatio-temporal solitons in an inhomogeneous nonlinear medium (e.g., cubic nonlinear Schrödinger equation with the self-focusing and defocusing cases). Exact analytical solitons are derived in both one-dimensional (1D) and higher-dimensional (e.g., 2D, 3D) geometries such that they are verified to be stable in the given parameters regions. Particularly, several families of numerical fundamental solitons (especially the 1D double-peaked solitons, 2D vortex solitons, and 3D double bullets) can be found to be stable around the propagation parameters for exact solitons. Other significant properties of solitons are also explored including the interactions of solitons, stable soliton excitations, and transverse power flows. The results may excite the corresponding theoretical analysis and experiment designs.

Massive soliton stars

NASA Technical Reports Server (NTRS)

Chiu, Hong-Yee

1990-01-01

The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.

Stationary states of fermions in a sign potential with a mixed vector–scalar coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castilho, W.M., E-mail: castilho.w@gmail.com; Castro, A.S. de, E-mail: castro@pq.cnpq.br

2014-01-15

The scattering of a fermion in the background of a sign potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling under the Sturm–Liouville perspective. When the vector coupling and the scalar coupling have different magnitudes, an isolated solution shows that the fermion under a strong potential can be trapped in a highly localized region without manifestation of Klein’s paradox. It is also shown that the lonely bound-state solution disappears asymptotically as one approaches the conditions for the realization of spin and pseudospin symmetries. --more » Highlights: •Scattering of fermions in a sign potential assessed under a Sturm–Liouville perspective. •An isolated bounded solution. •No pair production despite the high localization. •No bounded solution under exact spin and pseudospin symmetries.« less

The wrinkle-like N-solitons for the thermophoretic motion equation through graphene sheets

NASA Astrophysics Data System (ADS)

Ma, Yu-Lan; Li, Bang-Qing

2018-03-01

The main work is focused on the thermophoretic motion equation, which was derived from wrinkle wave motions in substrate-supported graphene sheets. Via the bilinear method, a class of wrinkle-like N-soliton solutions is constructed. The one-soliton, two-soliton and three-soliton are observed graphically. The shape, amplitude, open direction and width of the N-solitons are controllable through certain parameters.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation in the fluid/plasma mechanics

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Wang, Qi-Min

2016-09-01

Under investigation in this paper is a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation for the shallow water wave in a fluid or electrostatic wave potential in a plasma. Bilinear form, Bäcklund transformation and Lax pair are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota’s method. Propagation and interaction of the solitons are illustrated graphically: (i) Through the asymptotic analysis, elastic and inelastic interactions between the two solitons are discussed analytically and graphically, respectively. The elastic interaction, amplitudes, velocities and shapes of the two solitons remain unchanged except for a phase shift. However, in the area of the inelastic interaction, amplitudes of the two solitons have a linear superposition. (ii) Elastic interactions among the three solitons indicate that the properties of the elastic interactions among the three solitons are similar to those between the two solitons. Moreover, oblique and overtaking interactions between the two solitons are displayed. Oblique interactions among the three solitons and interactions among the two parallel solitons and a single one are presented as well. (iii) Inelastic-elastic interactions imply that the interaction between the inelastic region and another one is elastic.

Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient

NASA Astrophysics Data System (ADS)

Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.

2017-09-01

We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.

Reduced conservatism in stability robustness bounds by state transformation

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.; Liang, Z.

1986-01-01

This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.

Reconfigurable Network Routing with Spatial Soliton Crossbar Switches

DTIC Science & Technology

1999-01-31

Properties of Quadratic Solitons", Acta Physica Polonica , in press 32. G.I. Stegeman and M. Segev, "Bright Spatial Soliton Interactions", book chapter for...put and output poVts. the central idea is to use the solitons as a waveguide for guiding signals. Deflecting the soliton electro-optically...as reconfigurable interconnects for guiding signals between multiple input and output ports. The central idea is to use the solitons as a waveguide

Surface dark screening solitons.

PubMed

Chen, W Q; Yang, X; Zhong, S Y; Yan, Z; Zhang, T H; Tian, J G; Xu, J J

2011-10-01

We report on the existence of surface dark screening solitons at the interface between a dielectric medium (air) and a self-defocusing nonlinear material, taking advantage of photorefractive diffusion and drift nonlinearities. It is very interesting that a surface dark soliton is just like half of a dark soliton in bulk, but not a whole dark soliton propagating along surface. The excitation, propagation, and stability of this type of soliton are studied by using the beam-propagation method. Another interesting thing is that this type of dark soliton can be excited by a planar light beam without a necessary dark notch. © 2011 Optical Society of America

Dark solitons in laser radiation build-up dynamics.

PubMed

Woodward, R I; Kelleher, E J R

2016-03-01

We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice.

PubMed

Takahashi, Daisuke A

2016-06-01

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

Rational solitons in deep nonlinear optical Bragg grating.

PubMed

Alatas, H; Iskandar, A A; Tjia, M O; Valkering, T P

2006-06-01

We have examined the rational solitons in the Generalized Coupled Mode model for a deep nonlinear Bragg grating. These solitons are the degenerate forms of the ordinary solitons and appear at the transition lines in the parameter plane. A simple formulation is presented for the investigation of the bifurcations induced by detuning the carrier wave frequency. The analysis yields among others the appearance of in-gap dark and antidark rational solitons unknown in the nonlinear shallow grating. The exact expressions for the corresponding rational solitons are also derived in the process, which are characterized by rational algebraic functions. It is further demonstrated that certain effects in the soliton energy variations are to be expected when the frequency is varied across the values where the rational solitons appear.

Solitons interaction and integrability for a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Guo, Yong-Jiang; Li, Hui-Min

2018-03-01

Under investigation in this paper is a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves. Via the symbolic computation, Bell polynomials and Hirota method, the Bäcklund transformation, Lax pair, bilinear forms, one- and two-soliton solutions are derived. Propagation and interaction for the solitons are illustrated: Amplitudes and shapes of the one soliton keep invariant during the propagation, which implies that the transport of the energy is stable for the (2+1)-dimensional water waves; and inelastic interactions between the two solitons are discussed. Elastic interactions between the two parabolic-, cubic- and periodic-type solitons are displayed, where the solitonic amplitudes and shapes remain unchanged except for certain phase shifts. However, inelastically, amplitudes of the two solitons have a linear superposition after each interaction which is called as a soliton resonance phenomenon.

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Wenjun; Tian Bo, E-mail: tian.bupt@yahoo.com.c; State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191

2010-08-15

Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed withmore » the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.« less

Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

2015-11-01

Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

Investigation on nonautonomous soliton management in generalized external potentials via dispersion and nonlinearity

NASA Astrophysics Data System (ADS)

Vijayalekshmi, S.; Mani Rajan, M. S.; Mahalingam, A.; Uthayakumar, A.

2015-09-01

We investigate the controllable behavior of nonautonomous soliton in external potentials with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous fiber system. We derive the Lax pair with a variable spectral parameter and the exact multi-soliton solution is generated via Darboux transformation. Based on these solutions, several novel optical solitons are constructed by selecting appropriate functions and the main evolution features of these waves are shown by some interesting figures with computer simulation. As few examples, breathers in periodic potential, soliton compression in an exponentially dispersion decreasing fiber and interaction of boomerang solitons are discussed. The presented results have applications in the study of nonautonomous soliton birefringence-managed switching architecture. These results are potentially useful in the management of nonautonomous soliton with external potentials in the optical soliton communications and long-haul telecommunication networks.

Multi-hump bright solitons in a Schrödinger-mKdV system

NASA Astrophysics Data System (ADS)

Cisneros-Ake, Luis A.; Parra Prado, Hugo; López Villatoro, Diego Joselito; Carretero-González, R.

2018-03-01

We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg-de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS-mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.

Theory of the deformation of aligned polyethylene.

PubMed

Hammad, A; Swinburne, T D; Hasan, H; Del Rosso, S; Iannucci, L; Sutton, A P

2015-08-08

Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel-Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the introduction of tensile and compressive solitons at the chain ends to mark the onset of plasticity at a well-defined yield stress, which is much less than the theoretical pull-out stress. Interaction energies between solitons and an equation of motion for solitons are derived. The equation of motion is based on Langevin dynamics and the fluctuation-dissipation theorem and it leads to the rigorous definition of an effective mass for solitons. It forms the basis of a soliton dynamics in direct analogy to dislocation dynamics. Close parallels are drawn between solitons in aligned polymers and dislocations in crystals, including the configurational force on a soliton. The origins of the strain rate and temperature dependencies of the viscoelastic behaviour are discussed in terms of the formation energy of solitons. A failure mechanism is proposed involving soliton condensation under a tensile load.

Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Haifeng; Wang Shiqing; Engineering and Technical College of Chengdu University of Technology, Leshan 614000

2011-04-15

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev-Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.

Solitonic Dispersive Hydrodynamics: Theory and Observation

NASA Astrophysics Data System (ADS)

Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.

2018-04-01

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Yu-E.; Xue, Ju-Kui

2018-04-01

We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Chen, Manna; Ping, Xiaorou; Liang, Guo; Guo, Qi; Lu, Daquan; Hu, Wei

2018-01-01

Dark solitons are traditionally considered to exist in defocusing Kerr nonlinearity media. We investigate dark quadratic solitons with a focusing effective Kerr nonlinearity and a sine-oscillatory nonlocal response. A nonlinear refractive index with a focusing sine-oscillatory response leads to a defocusing effect with a strong degree of nonlocality, which causes the formation of dark solitons. By analyzing the modulational instability, we determine the parameter domain for dark quadratic solitons with a stable background and numerically obtain dark-bright soliton solutions in the form of pairs, which avoid radiative phenomena. Based on a numerical simulation, we find that all dark-bright soliton pairs are unstable after a relatively long propagation distance, and their stabilities are affected by the soliton interval and the degree of nonlocality.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biondini, Gino

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u{sub t}+6uu{sub x}+3u{sub xxx}){sub x}+u{sub yy}=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y{yields}{infinity} coincide with those of the N asymptotic line solitons as y{yields}-{infinity}. We also show that the (2N-1){exclamation_point}{exclamation_point} types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.

Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

NASA Astrophysics Data System (ADS)

Pelinovsky, E. N.; Shurgalina, E. G.; Sergeeva, A. V.; Talipova, T. G.; El, G. A.; Grimshaw, R. H. J.

2013-01-01

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg-de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

NASA Astrophysics Data System (ADS)

Xu, Quan; Tian, Qiang

2005-04-01

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

Bright and dark N-soliton solutions for the (2 + 1)-dimensional Maccari system

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Yuan, Yu-Qiang; Sun, Yan

2018-02-01

Under investigation in this paper is the (2 + 1) -dimensional Maccari system, which is related to the Kadomtsev-Petviashvili (KP) equation. Bright and dark N -soliton solutions in terms of the Gramian are obtained via the KP hierarchy reduction. Oblique and parallel interactions between the bright solitons and between the dark solitons are studied analytically and graphically. We find that there are elastic and inelastic interactions for the bright solitons, but there are only elastic interactions for the dark solitons. Resonance, breather, attraction and repulsion structures are presented. It is expected that these soliton interactions have potential applications in fluid dynamics, nonlinear optics and plasma physics.

Brownian motion of solitons in a Bose–Einstein condensate

PubMed Central

Aycock, Lauren M.; Hurst, Hilary M.; Efimkin, Dmitry K.; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M.; Spielman, I. B.

2017-01-01

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated Rb87 Bose–Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton’s diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment. PMID:28196896

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Coexistence of a self-induced transparency soliton and a Bragg soliton.

PubMed

Tseng, Hong-Yih; Chi, Sien

2002-11-01

We theoretically show that a self-induced transparency (SIT) soliton and a Bragg soliton can coexist in a nonlinear photonic band gap (PBG) medium doped uniformly with inhomogeneous-broadening two-level atoms. The Maxwell-Bloch equations for the pulse propagating through such a uniformly doped PBG structure are derived first and further reduced to an effective nonlinear Schrödinger equation. This model describes an equivalent physical mechanism for a Bragg-soliton propagation resulting from the effective quadratic dispersion balancing with the effective third-order nonlinearity. Because the resonant atoms are taken into account, the original band gap can be shifted both by the dopants and the instantaneous nonlinearity response originating from an intense optical pulse. As a result, even if a SIT soliton with its central frequency deep inside the original forbidden band, it still can propagate through the resonant PBG medium as long as this SIT soliton satisfies the effective Bragg-soliton propagation. An approximate soliton solution describing such coexistence is found. We also show that the pulse width and group velocity of this soliton solution can be uniquely determined for given material parameters, atomic transition frequency, and input central frequency of the soliton. The numerical examples of the SIT soliton in a one-dimensional As2S3-based PBG structure doped uniformly with Lorentzian line-shape resonant atoms are shown. It is found that a SIT soliton with approximately 100-ps width in such a resonant PBG structure can travel with the velocity being two orders of magnitude slower than the light speed in an unprocessed host medium.

Intermode Breather Solitons in Optical Microresonators

NASA Astrophysics Data System (ADS)

Guo, Hairun; Lucas, Erwan; Pfeiffer, Martin H. P.; Karpov, Maxim; Anderson, Miles; Liu, Junqiu; Geiselmann, Michael; Jost, John D.; Kippenberg, Tobias J.

2017-10-01

Dissipative solitons can be found in a variety of systems resulting from the double balance between dispersion and nonlinearity, as well as gain and loss. Recently, they have been observed to spontaneously form in Kerr nonlinear microresonators driven by a continuous wave laser, providing a compact source of coherent optical frequency combs. As optical microresonators are commonly multimode, intermode interactions, which give rise to avoided mode crossings, frequently occur and can alter the soliton properties. Recent works have shown that avoided mode crossings cause the soliton to acquire a single-mode dispersive wave, a recoil in the spectrum, or lead to soliton decay. Here, we show that avoided mode crossings can also trigger the formation of breather solitons, solitons that undergo a periodic evolution in their amplitude and duration. This new breather soliton, referred to as an intermode breather soliton, occurs within a laser detuning range where conventionally stationary (i.e., stable) dissipative Kerr solitons are expected. We experimentally demonstrate the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators) and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We show that the breathing is associated with a periodic energy exchange between the soliton and a second optical mode family, a behavior that can be modeled by a response function acting on dissipative solitons described by the Lugiato-Lefever model. The observation of breathing dynamics in the conventionally stable soliton regime is relevant to applications in metrology such as low-noise microwave generation, frequency synthesis, or spectroscopy.

Dark soliton fiber lasers.

PubMed

Tang, Dingyuan; Guo, Jun; Song, Yufeng; Zhang, Han; Zhao, Luming; Shen, Deyuan

2014-08-11

Dark soliton formation and soliton dynamics in all-normal dispersion cavity fiber ring lasers without an anti-saturable absorber in cavity is studied both theoretically and numerically. It is shown that under suitable conditions the dark solitons formed could be described by the nonlinear Schrödinger equation. The dark soliton formation in an all-normal-dispersion cavity erbium-doped fiber ring laser without an anti-saturable absorber in cavity is first experimentally demonstrated. Individual dark solitons are experimentally identified. Excellent agreement between theory and experiment is observed.

Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons

NASA Astrophysics Data System (ADS)

Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.

Bright solitons for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

NASA Astrophysics Data System (ADS)

Xie, Xi-Yang; Tian, Bo; Liu, Lei; Guan, Yue-Yang; Jiang, Yan

2017-06-01

In this paper, we investigate a generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. Under certain integrable constraints, bilinear forms, bright one- and two-soliton solutions are obtained. Via certain transformation, we investigate the properties of the solitons with the first-order dispersion parameter σ1(x, t), second-order dispersion parameter σ2(x, t), third-order dispersion parameter σ3(x, t), phase modulation and gain (loss) v(x, t). Soliton propagation and collision are graphically presented and analyzed: One soliton is shown to maintain its amplitude and width during the propagation. When we choose σ1(x, t), σ2(x, t) and σ3(x, t) differently, travelling direction of the soliton is found to alter. v(x, t) is observed to affect the amplitude of the soliton. Head-on collision between the two solitons is presented with σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) as the constants, and solitons' amplitudes are the same before and after the collision. When σ1(x, t), σ2(x, t) and σ3(x, t) are chosen as certain functions, the solitons' traveling directions change during the collision. v(x, t) can influence the amplitudes of the two solitons.

Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators

NASA Astrophysics Data System (ADS)

Guo, H.; Karpov, M.; Lucas, E.; Kordts, A.; Pfeiffer, M. H. P.; Brasch, V.; Lihachev, G.; Lobanov, V. E.; Gorodetsky, M. L.; Kippenberg, T. J.

2017-01-01

Temporal dissipative Kerr solitons in optical microresonators enable the generation of ultrashort pulses and low-noise frequency combs at microwave repetition rates. They have been demonstrated in a growing number of microresonator platforms, enabling chip-scale frequency combs, optical synthesis of low-noise microwaves and multichannel coherent communications. In all these applications, accessing and maintaining a single-soliton state is a key requirement--one that remains an outstanding challenge. Here, we study the dynamics of multiple-soliton states and report the discovery of a simple mechanism that deterministically switches the soliton state by reducing the number of solitons one by one. We demonstrate this control in Si3N4 and MgF2 resonators and, moreover, we observe a secondary peak to emerge in the response of the system to a pump modulation, an effect uniquely associated with the soliton regime. Exploiting this feature, we map the multi-stability diagram of a microresonator experimentally. Our measurements show the physical mechanism of the soliton switching and provide insight into soliton dynamics in microresonators. The technique provides a method to sequentially reduce, monitor and stabilize an arbitrary state with solitons, in particular allowing for feedback stabilization of single-soliton states, which is necessary for practical applications.

Optical spatial solitons at the interface between two dissimilar periodic media: theory and experiment.

PubMed

Suntsov, S; Makris, K G; Christodoulides, D N; Stegeman, G I; Morandotti, R; Volatier, M; Aimez, V; Arès, R; Yang, E H; Salamo, G

2008-07-07

Discrete spatial solitons traveling along the interface between two dissimilar one-dimensional arrays of waveguides were observed for the first time. Two interface solitons were found theoretically, each one with a peak in a different boundary channel. One evolves into a soliton from a linear mode at an array separation larger than a critical separation where-as the second soliton always exhibits a power threshold. These solitons exhibited different power thresholds which depended on the characteristics of the two lattices. For excitation of single channels near and at the boundary, the evolution behavior with propagation distance indicates that the solitons peaked near and at the interface experience an attractive potential on one side of the boundary, and a repulsive one on the opposite side. The power dependence of the solitons at variable distance from the boundary was found to be quite different on opposite sides of the interface and showed evidence for soliton switching between channels with increasing input power.

Solitons riding on solitons and the quantum Newton's cradle.

PubMed

Ma, Manjun; Navarro, R; Carretero-González, R

2016-02-01

The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.

CLASSICAL AREAS OF PHENOMENOLOGY: Temporal behaviour of open-circuit photovoltaic solitons

NASA Astrophysics Data System (ADS)

Zhang, Mei-Zhi; Lu, Ke-Qing; Cheng, Guang-Hua; Li, Ke-Hao; Zhang, Yi-Qi; Zhang, Yu-Hong; Zhang, Yan-Peng

2009-07-01

Based on the time-dependent band-transport model in a photorefractive medium, dark open-circuit photovoltaic (PV) solitons are investigated both theoretically and experimentally. Compared with those of the time-independent models, our theoretical results revealed that quasi-steady-state and steady-state PV solitons can both be obtained. Our results also revealed that when r < 1 (r is the normalized intensity at infinity), the full width at half maximum (FWHM) of solitons decreases monotonically to a constant value; when r > 1, however, the FWHM of solitons first decreases to a minimum before it increases to a constant value. Moreover, the FWHM of steady solitons decreases with increasing intensity ratio for r < 1, and increases with increasing intensity ratio for r > 1. We further observed dark PV solitons in experiments, and recorded their evolution. These results indicated that steady solitons can be observed at low optical power, while quasi-steady-state solitons can only be generated at higher optical power. Good agreement is found between theory and experiment.

Quantum many-body dynamics of dark solitons in optical lattices

NASA Astrophysics Data System (ADS)

Mishmash, R. V.; Danshita, I.; Clark, Charles W.; Carr, L. D.

2009-11-01

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system’s natural orbitals.

Dark soliton beats in the time-varying background of Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu Lei; Li Lu; Zhang Jiefang

2009-07-15

We investigate the dynamics of dark solitons in one-dimensional Bose-Einstein condensates. In the large particle limit, by introducing the lens-type transformation, we find that the macroscopic wave function evolves self-similarly when its initial profile strays from that of the equilibrium state, which provides a time-varying background for the propagation of dark solitons. The interaction of dark solitons with this kind of background is studied both analytically and numerically. We find that the center-of-mass motion of the dark soliton is deeply affected by the time-varying background, and the beating phenomena of dark soliton emerge when the intrinsic frequency of the darkmore » soliton approaches that of the background. Lastly, we investigate the propagation of dark solitons in the freely expanding background.« less

Accessible solitons of fractional dimension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874, Doha; Belić, Milivoj

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential.more » •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.« less

Fate of a gray soliton in a quenched Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Gamayun, O.; Bezvershenko, Yu. V.; Cheianov, V.

2015-03-01

We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the nonlinearity parameter. The outcome of the quench is found to depend dramatically on the ratio η of the final and initial values of the speed of sound. For integer η the soliton splits into exactly 2 η -1 solitons. For noninteger η the soliton decays into multiple solitons and Bogoliubov modes. The case of integer η is analyzed in detail. The parameters of solitons in the out state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for similar quenches in any classical integrable system.

Oblique collision of dust acoustic solitons in a strongly coupled dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boruah, A.; Sharma, S. K., E-mail: sumita-sharma82@yahoo.com; Bailung, H.

2015-09-15

The oblique collision between two equal amplitude dust acoustic solitons is observed in a strongly coupled dusty plasma. The solitons are subjected to oblique interaction at different colliding angles. We observe a resonance structure during oblique collision at a critical colliding angle which is described by the idea of three wave resonance interaction modeled by Kadomtsev-Petviashvili equation. After collision, the solitons preserve their identity. The amplitude of the resultant wave formed during interaction is measured for different collision angles as well as for different colliding soliton amplitudes. At resonance, the maximum amplitude of the new soliton formed is nearly 3.7more » times the initial soliton amplitude.« less

Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser

NASA Astrophysics Data System (ADS)

Liu, Meng; Li, Heng; Luo, Ai-Ping; Cui, Hu; Xu, Wen-Cheng; Luo, Zhi-Chao

2018-03-01

Ultrafast fiber lasers have been demonstrated to be great platforms for the investigation of soliton dynamics. The soliton molecules, as one of the most fascinating nonlinear phenomena, have been a hot topic in the field of nonlinear optics in recent years. Herein, we experimentally observed the real-time evolving behavior of soliton molecule in an ultrafast fiber laser by using the dispersive Fourier transformation technology. Several types of evolving soliton molecules were obtained in our experiments, such as soliton molecules with monotonically or chaotically evolving phase, flipping and hopping phase. These results would be helpful to the communities interested in soliton nonlinear dynamics as well as ultrafast laser technologies.

Exact soliton solutions and their stability control in the nonlinear Schrödinger equation with spatiotemporally modulated nonlinearity.

PubMed

Tian, Qing; Wu, Lei; Zhang, Jie-Fang; Malomed, Boris A; Mihalache, D; Liu, W M

2011-01-01

We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton's eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.

3D simulation for solitons used in optical fibers

NASA Astrophysics Data System (ADS)

Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.

2016-12-01

In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.

Soliton creation, propagation, and annihilation in aeromechanical arrays of one-way coupled bistable elements

NASA Astrophysics Data System (ADS)

Rosenberger, Tessa; Lindner, John F.

We study the dynamics of mechanical arrays of bistable elements coupled one-way by wind. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Soliton-like waves propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in even arrays where adjacent elements are attracted to opposite stable states. Solitons propagate indefinitely in odd arrays where pairing is frustrated. Large noise spontaneously creates soliton- antisoliton pairs, as predicted by prior computer simulations. Soliton annihilation times increase quadratically with initial separations, as expected for random walk models of soliton collisions.

Helmholtz dark solitons.

PubMed

Chamorro-Posada, P; McDonald, G S

2003-05-15

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Broer-Kaup-Kupershmidt system in the shallow water of uniform depth

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Mao, Bing-Qing

2017-03-01

Under investigation in this paper is a (2+1)-dimensional Broer-Kaup-Kupershmidt system for the nonlinear and dispersive long gravity waves on two horizontal directions in the shallow water of uniform depth. Bilinear forms, Bäcklund transformation and Lax pair are derived based on the Bell polynomials and symbolic computation. One- and two-soliton solutions with a real function ϕ(y) are constructed via the Hirota method, where y is the scaled space coordinate. Propagation and interaction of the solitons are illustrated graphically: (i) ϕ(y) affects the shape of the solitons. (ii) Interaction of the solitons including the elastic and inelastic interactions are discussed. When the solitons' interaction is elastic, the amplitude, velocity and shape of the soliton remain invariant after the interaction except for a phase shift, and the smaller-amplitude soliton has a larger phase shift. (iii) Height of the water surface above a horizontal bottom can be a bell-shaped soliton or an upside-down bell-shaped soliton under certain conditions, while horizontal velocity of the water wave always keeps bell-shaped.

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

NASA Astrophysics Data System (ADS)

de Oliveira, Luiz P.

2016-09-01

The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff-Snyder-Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles.

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Xin, E-mail: yuxin@buaa.edu.cn; Sun, Zhi-Yuan

Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

NASA Astrophysics Data System (ADS)

Yu, Xin; Sun, Zhi-Yuan

2016-04-01

Under investigation in this paper is a nonautonomous Kadomtsev-Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser.

PubMed

Peng, Junsong; Tarasov, Nikita; Sugavanam, Srikanth; Churkin, Dmitry

2016-09-19

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates.

PubMed

Parker, N G; Proukakis, N P; Leadbeater, M; Adams, C S

2003-06-06

Longitudinal confinement of dark solitons in quasi-one-dimensional Bose-Einstein condensates leads to sound emission and reabsorption. We perform quantitative studies of the dynamics of a soliton oscillating in a tight dimple trap, embedded in a weaker harmonic trap. The dimple depth provides a sensitive handle to control the soliton-sound interaction. In the limit of no reabsorption, the power radiated is found to be proportional to the soliton acceleration squared. An experiment is proposed to detect sound emission as a change in amplitude and frequency of soliton oscillations.

Dark solitons at nonlinear interfaces.

PubMed

Sánchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S

2010-05-01

The refraction of dark solitons at a planar boundary separating two defocusing Kerr media is simulated and analyzed, for the first time (to our knowledge). Analysis is based on the nonlinear Helmholtz equation and is thus valid for any angle of incidence. A new law, governing refraction of black solitons, is combined with one describing bright soliton refraction to yield a generalized Snell's law whose validity is verified numerically. The complexity of gray soliton refraction is also analyzed, and illustrated by a change from external to internal refraction on varying the soliton contrast parameter.

Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations.

PubMed

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M; Liu, Yi; Grelu, Philippe

2016-06-01

We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.

Rogue waves and lump solitons for a ?-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Yin, Hui-Min

2018-07-01

Under investigation is a ?-dimensional B-type Kadomtsev-Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, ?, increasing when ?. In addition, dark rogue waves are derived when ?. Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter ?, and amplitude of the lump soliton is negatively correlated with ? when ?.

Lump and rogue waves for the variable-coefficient Kadomtsev-Petviashvili equation in a fluid

NASA Astrophysics Data System (ADS)

Jia, Xiao-Yue; Tian, Bo; Du, Zhong; Sun, Yan; Liu, Lei

2018-04-01

Under investigation in this paper is the variable-coefficient Kadomtsev-Petviashvili equation, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Employing the bilinear form and symbolic computation, we obtain the lump, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions. Discussions indicate that the variable coefficients are related to both the lump soliton’s velocity and amplitude. Mixed lump-stripe soliton solutions display two different properties, fusion and fission. Mixed rogue wave-stripe soliton solutions show that a rogue wave arises from one of the stripe solitons and disappears into the other. When the time approaches 0, rogue wave’s energy reaches the maximum. Interactions between a lump soliton and one-stripe soliton, and between a rogue wave and a pair of stripe solitons, are shown graphically.

Novel tunable dynamic tweezers using dark-bright soliton collision control in an optical add/drop filter.

PubMed

Teeka, Chat; Jalil, Muhammad Arif; Yupapin, Preecha P; Ali, Jalil

2010-12-01

We propose a novel system of the dynamic optical tweezers generated by a dark soliton in the fiber optic loop. A dark soliton known as an optical tweezer is amplified and tuned within the microring resonator system. The required tunable tweezers with different widths and powers can be controlled. The analysis of dark-bright soliton conversion using a dark soliton pulse propagating within a microring resonator system is analyzed. The dynamic behaviors of soliton conversion in add/drop filter is also analyzed. The control dark soliton is input into the system via the add port of the add/drop filter. The dynamic behavior of the dark-bright soliton conversion is observed. The required stable signal is obtained via a drop and throughput ports of the add/drop filter with some suitable parameters. In application, the trapped light/atom and transportation can be realized by using the proposed system.

Optical Quasi-Soliton Solutions for the Cubic-Quintic Nonlinear SCHRÖDINGER Equation with Variable Coefficients

NASA Astrophysics Data System (ADS)

Yang, Qin; Zhang, Jie-Fang

Optical quasi-soliton solutions for the cubic-quintic nonlinear Schrödinger equation (CQNLSE) with variable coefficients are considered. Based on the extended tanh-function method, we not only successfully obtained bright and dark quasi-soliton solutions, but also obtained the kink quasi-soliton solutions under certain parametric conditions. We conclude that the quasi-solitons induced by the combined effects of the group velocity dispersion (GVD) distribution, the nonlinearity distribution, higher-order nonlinearity distribution, and the amplification or absorption coefficient are quite different from those of the solitons induced only by the combined effects of the GVD, the nonlinearity distribution, and the amplification or absorption coefficient without considering the higher-order nonlinearity distribution (i.e. α(z)=0). Furthermore, we choose appropriate optical fiber parameters D(z) and R(z) to control the velocity of quasi-soliton and time shift, and discuss the evolution behavior of the special quasi-soliton.

Single-mode dispersive waves and soliton microcomb dynamics

PubMed Central

Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry

2017-01-01

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications. PMID:28332495

Constraints on primordial magnetic fields from inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Green, Daniel; Kobayashi, Takeshi, E-mail: drgreen@cita.utoronto.ca, E-mail: takeshi.kobayashi@sissa.it

2016-03-01

We present generic bounds on magnetic fields produced from cosmic inflation. By investigating field bounds on the vector potential, we constrain both the quantum mechanical production of magnetic fields and their classical growth in a model independent way. For classical growth, we show that only if the reheating temperature is as low as T{sub reh} ∼< 10{sup 2} MeV can magnetic fields of 10{sup −15} G be produced on Mpc scales in the present universe. For purely quantum mechanical scenarios, even stronger constraints are derived. Our bounds on classical and quantum mechanical scenarios apply to generic theories of inflationary magnetogenesis with a two-derivative timemore » kinetic term for the vector potential. In both cases, the magnetic field strength is limited by the gravitational back-reaction of the electric fields that are produced simultaneously. As an example of quantum mechanical scenarios, we construct vector field theories whose time diffeomorphisms are spontaneously broken, and explore magnetic field generation in theories with a variable speed of light. Transitions of quantum vector field fluctuations into classical fluctuations are also analyzed in the examples.« less

The fate of a gray soliton in a quenched Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Gamayun, Oleksandr; Bezvershenko, Yulia; Cheianov, Vadim

2015-03-01

We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the non-linearity parameter. The outcome of the quench is found to depend dramatically on the ratio η of the final and initial values of the speed of sound. For integer η the soliton splits into exactly 2 η - 1 solitons. For non-integer η the soliton decays into multiple solitons and Bogoliubov modes. The case of integer η is analyzed in detail. The parameters of solitons in the out-state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for the similar quenches in any classical integrable system.

Fusion and fission phenomena for the soliton interactions in a plasma

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Wu, Xiao-Yu; Liu, Lei

2017-02-01

Investigation in this paper is given to a generalized (3 + 1) -dimensional variable-coefficient Kadomtsev-Petviashvili equation for a plasma. Via the bilinear form, the singular and double Wronskian soliton solutions are derived, respectively, under the different variable-coefficient constraints. Interactions between the two solitons are depicted, where the soliton fusion and fission phenomena are respectively pictured out, both for the velocity-unvarying and velocity-varying two solitons. Soliton velocity is related to the variable coefficients h( t), l ( t), q( t), m( t) and n( t), while the soliton amplitude is not affected by them, where h( t), l( t) and q( t) are the perturbed effects, m( t) and n( t) stand for the disturbed wave velocities along the transverse spatial coordinates.

Interactions of bright and dark solitons with localized PT-symmetric potentials.

PubMed

Karjanto, N; Hanif, W; Malomed, B A; Susanto, H

2015-02-01

We study collisions of moving nonlinear-Schrödinger solitons with a PT-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solitons are found by means of numerical simulations, and in the approximate semi-analytical form. An exact solution for the dark soliton pinned by the complex PT-symmetric dipole is produced too.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

PubMed

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

Three-dimensional vortex-bright solitons in a spin-orbit-coupled spin-1 condensate

NASA Astrophysics Data System (ADS)

Gautam, Sandeep; Adhikari, S. K.

2018-01-01

We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground state. We also numerically investigate moving solitons. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed mean-field model for generating the moving solitons.

Adiabatic Soliton Laser

NASA Astrophysics Data System (ADS)

Bednyakova, Anastasia; Turitsyn, Sergei K.

2015-03-01

The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity—the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.

Soliton and kink jams in traffic flow with open boundaries.

PubMed

Muramatsu, M; Nagatani, T

1999-07-01

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.

Different Vaccine Vectors Delivering the Same Antigen Elicit CD8plus T Cell Responses with Distinct Clonotype and Epitope Specificity

DOE Office of Scientific and Technical Information (OSTI.GOV)

M Honda; R Wang; W Kong

Prime-boost immunization with gene-based vectors has been developed to generate more effective vaccines for AIDS, malaria, and tuberculosis. Although these vectors elicit potent T cell responses, the mechanisms by which they stimulate immunity are not well understood. In this study, we show that immunization by a single gene product, HIV-1 envelope, with alternative vector combinations elicits CD8{sup +} cells with different fine specificities and kinetics of mobilization. Vaccine-induced CD8{sup +} T cells recognized overlapping third V region loop peptides. Unexpectedly, two anchor variants bound H-2D{sup d} better than the native sequences, and clones with distinct specificities were elicited by alternativemore » vectors. X-ray crystallography revealed major differences in solvent exposure of MHC-bound peptide epitopes, suggesting that processed HIV-1 envelope gave rise to MHC-I/peptide conformations recognized by distinct CD8{sup +} T cell populations. These findings suggest that different gene-based vectors generate peptides with alternative conformations within MHC-I that elicit distinct T cell responses after vaccination.« less

Different Vaccine Vectors Delivering the Same Antigen Elicit CD8+ T Cell Responses with Distinct Clonotype and Epitope Specificity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Honda, M.; Robinson, H.; Wang, R.

Prime-boost immunization with gene-based vectors has been developed to generate more effective vaccines for AIDS, malaria, and tuberculosis. Although these vectors elicit potent T cell responses, the mechanisms by which they stimulate immunity are not well understood. In this study, we show that immunization by a single gene product, HIV-1 envelope, with alternative vector combinations elicits CD8{sup +} cells with different fine specificities and kinetics of mobilization. Vaccine-induced CD8{sup +} T cells recognized overlapping third V region loop peptides. Unexpectedly, two anchor variants bound H-2D{sup d} better than the native sequences, and clones with distinct specificities were elicited by alternativemore » vectors. X-ray crystallography revealed major differences in solvent exposure of MHC-bound peptide epitopes, suggesting that processed HIV-1 envelope gave rise to MHC-I/peptide conformations recognized by distinct CD8{sup +} T cell populations. These findings suggest that different gene-based vectors generate peptides with alternative conformations within MHC-I that elicit distinct T cell responses after vaccination.« less

Multicomponent long-wave-short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons.

PubMed

Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M

2014-11-01

We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

Modeling the Gross-Pitaevskii Equation Using the Quantum Lattice Gas Method

NASA Astrophysics Data System (ADS)

Oganesov, Armen

We present an improved Quantum Lattice Gas (QLG) algorithm as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii (GP) equation for Bose-Einstein Condensates (BECs). The method employs an interleaved sequence of unitary collide and stream operators. QLG is applicable to many different scalar potentials in the weak interaction regime and has been used to model the Korteweg-de Vries (KdV), Burgers and GP equations. It can be implemented on both quantum and classical computers and is extremely scalable. We present results for 1D soliton solutions with positive and negative internal interactions, as well as vector solitons with inelastic scattering. In higher dimensions we look at the behavior of vortex ring reconnection. A further improvement is considered with a proper operator splitting technique via a Fourier transformation. This is great for quantum computers since the quantum FFT is exponentially faster than its classical counterpart which involves non-local data on the entire lattice (Quantum FFT is the backbone of the Shor algorithm for quantum factorization). We also present an imaginary time method in which we transform the Schrodinger equation into a diffusion equation for recovering ground state initial conditions of a quantum system suitable for the QLG algorithm.

Navier-Stokes dynamics on a differential one-form

NASA Astrophysics Data System (ADS)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

General properties and analytical approximations of photorefractive solitons

NASA Astrophysics Data System (ADS)

Geisler, A.; Homann, F.; Schmidt, H.-J.

2004-08-01

We investigate general properties of spatial 1-dimensional bright photorefractive solitons and discuss various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r. The case of dark solitons is also briefly addressed.

Structural dissipative solitons in passive mode-locked fiber lasers.

PubMed

Komarov, Andrey; Sanchez, François

2008-06-01

On the basis of numerical simulation of fiber laser passive mode locking with anomalous dispersion we have found the dissipative solitons with powerful pedestals having oscillating structure. The pedestal structure causes a complex structural spectrum. These solitons can be multistable: with the same laser parameters the pedestals can have different structures. For some nonlinear-dispersion parameters there exist solitons with asymmetric structural pedestals moving relatively solitons with symmetric ones.

Many-body matter-wave dark soliton.

PubMed

Delande, Dominique; Sacha, Krzysztof

2014-01-31

The Gross-Pitaevskii equation--which describes interacting bosons in the mean-field approximation--possesses solitonic solutions in dimension one. For repulsively interacting particles, the stationary soliton is dark, i.e., is represented by a local density minimum. Many-body effects may lead to filling of the dark soliton. Using quasiexact many-body simulations, we show that, in single realizations, the soliton appears totally dark although the single particle density tends to be uniform.

Enhanced mutual capture of colored solitons by matched modulator

NASA Astrophysics Data System (ADS)

Feigenbaum, Eyal; Orenstein, Meir

2004-08-01

The mutual capture of two colored solitons is enhanced by a modulator, to a level which enables its practical exploitation, e.g., for a read- write mechanism in a soliton buffer. The enhanced capture was analyzed using closed form particle-like soliton perturbation, and verified by numerical simulations. Optimal modulator frequency and modulation depth are obtained. This mutual capture can be utilized for all-optical soliton logic and memory.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Traveling wave and soliton solutions of coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients.

PubMed

Zhong, Wei-Ping; Belić, Milivoj

2010-10-01

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

Stable gray soliton pinned by a defect in a microcavity-polariton condensate.

PubMed

Chen, Ting-Wei; Hsieh, Wen-Feng; Cheng, Szu-Cheng

2015-09-21

We study the spatially localized dark state, called dark soliton, in a one-dimensional system of the non-resonantly pumped microcavity-polariton condensate (MPC). From the recent work by Xue and Matuszewski [Phys. Rev. Lett. 112, 216401 (2014)], we know that the dark soliton in the pure MPC system is unstable. But we find that a dark soliton pinned by a defect in the impure MPC becomes a gray soliton and can be stabilized by the presence of a defect. Moreover, the stable regime of the gray soliton is given in terms of the defect strength and pump parameter.

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Zaidong; Li Qiuyan

2007-08-15

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schroedinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.

Matter-wave solitons in nonlinear optical lattices

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Malomed, Boris A.

2005-10-01

We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin , necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A , the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

Higher dimensional Taub-NUT spaces and applications

NASA Astrophysics Data System (ADS)

Stelea, Cristian Ionut

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden SL(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the C-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalising the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalisations of Kaluza-Klein magnetic monopoles, generalising the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalising the known Reissner-Nordstrom solutions.

Formation of quasiparallel Alfven solitons

NASA Technical Reports Server (NTRS)

Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.

1992-01-01

The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.

Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids.

PubMed

Muñoz Mateo, A; Brand, J

2014-12-19

Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.

Dark soliton synthesis using an optical pulse synthesizer and transmission through a normal-dispersion optical fiber.

PubMed

Kashiwagi, Ken; Mozawa, Kiyonobu; Tanaka, Yosuke; Kurokawa, Takashi

2013-12-16

We precisely generate dark solitons using an optical pulse synthesizer (OPS) at a repetition rate of 25 GHz and experimentally investigate soliton transmission through a normal-dispersion fiber. Because of their particular waveform, there are not many experimental studies. The OPS provides frequency-domain line-by-line modulation and produces arbitrary pulse waveforms. The soliton waveform has an intensity contrast greater than 20 dB. At certain input peak power, the pulse exhibits soliton transmission and maintains its initial waveform. The power agrees with soliton transmission theory. We confirm that the π phase shift at the center of the dark soliton is maintained after transmission through the fiber. We also investigate the influence of stimulated Brillouin scattering for long-distance transmission.

Solitonic Josephson Thermal Transport

NASA Astrophysics Data System (ADS)

Guarcello, Claudio; Solinas, Paolo; Braggio, Alessandro; Giazotto, Francesco

2018-03-01

We explore the coherent thermal transport sustained by solitons through a long Josephson junction as a thermal gradient across the system is established. We observe that a soliton causes the heat current through the system to increase. Correspondingly, the junction warms up in conjunction with the soliton, with temperature peaks up to, e.g., approximately 56 mK for a realistic Nb-based proposed setup at a bath temperature Tbath=4.2 K . The thermal effects on the dynamics of the soliton are also discussed. Markedly, this system inherits the topological robustness of the solitons. In view of these results, the proposed device can effectively find an application as a superconducting thermal router in which the thermal transport can be locally mastered through solitonic excitations, whose positions can be externally controlled through a magnetic field and a bias current.

Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

NASA Astrophysics Data System (ADS)

Ming, Yi; Ye, Liu; Chen, Han-Shuang; Mao, Shi-Feng; Li, Hui-Min; Ding, Ze-Jun

2018-01-01

Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-α β lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.

Statics and dynamics of atomic dark-bright solitons in the presence of impurities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Achilleos, V.; Frantzeskakis, D. J.; Kevrekidis, P. G.

2011-11-15

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with resultsmore » obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.« less

Cascade of Solitonic Excitations in a Superfluid Fermi Gas: From Solitons and Vortex Rings to Solitonic Vortices

NASA Astrophysics Data System (ADS)

Ku, Mark; Mukherjee, Biswaroop; Yefsah, Tarik; Zwierlein, Martin

2015-05-01

We follow the evolution of a superfluid Fermi gas of 6Li atoms following a one-sided π phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, and its subsequent snaking and decay into a vortex ring. The latter eventually breaks at the boundary of the superfluid, finally leaving behind a single, remnant solitonic vortex. The nodal surface is directly imaged and reveals its decay into a vortex ring via a puncture of the initial soliton plane. At intermediate stages we find evidence for more exotic structures resembling Φ-solitons. The observed evolution of the nodal surface represents dynamics that occurs at the length scale of the interparticle spacing, thus providing new experimental input for microscopic theories of strongly correlated fermions.

Chladni Solitons and the Onset of the Snaking Instability for Dark Solitons in Confined Superfluids

NASA Astrophysics Data System (ADS)

Muñoz Mateo, A.; Brand, J.

2014-12-01

Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ , and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.

Peregrine soliton generation and breakup in standard telecommunications fiber.

PubMed

Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Morin, Philippe; Fatome, Julien; Dudley, John M; Millot, Guy

2011-01-15

We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of nonideal initial conditions is studied through direct cutback measurements of the longitudinal evolution of the emerging soliton dynamics and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.

Multifrequency Gap Solitons in Nonlinear Photonic Crystals

NASA Astrophysics Data System (ADS)

Xie, Ping; Zhang, Zhao-Qing

2003-11-01

We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.

Analytical study on the generalized Davydov model in the alpha helical proteins

NASA Astrophysics Data System (ADS)

Wang, Pan; Xiao, Shu-Hong; Chen, Li; Yang, Gang

2017-06-01

In this paper, we investigate the dynamics of a generalized Davydov model derived from an infinite chain of alpha helical protein molecules which contain three hydrogen bonding spines running almost parallel to the helical axis. Through the introduction of the auxiliary function, the bilinear form, one-, two- and three-soliton solutions for the generalized Davydov model are obtained firstly. Propagation and interactions of solitons have been investigated analytically and graphically. The amplitude of the soliton is only related to the complex parameter μ and real parameter 𝜃 with a range of [0, 2π]. The velocity of the soliton is only related to the complex parameter μ, real parameter 𝜃, lattice parameter 𝜀, and physical parameters β1, β3 and β4. Overtaking and head-on interactions of two and three solitons are presented. The common in the interactions of three solitons is the directions of the solitons change after the interactions. The soliton derived in this paper is expected to have potential applications in the alpha helical proteins.

Beating dark-dark solitons and Zitterbewegung in spin-orbit-coupled Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Achilleos, V.; Frantzeskakis, D. J.; Kevrekidis, P. G.

2014-03-01

We present families of beating dark-dark solitons in spin-orbit (SO) -coupled Bose-Einstein condensates. These families consist of solitons residing simultaneously in the two bands of the energy spectrum. The soliton components are characterized by two different spatial and temporal scales, which are identified by a multiscale expansion method. The solitons are "beating" ones, as they perform density oscillations. The characteristic frequency of the latter is relevant to Zitterbewegung (ZB) oscillations, which were recently observed in experiments with SO-coupled condensates [C. Qu et al., Phys. Rev. A 88, 021604(R) (2013), 10.1103/PhysRevA.88.021604; L. J. LeBlanc et al., New J. Phys. 15, 073011 (2013), 10.1088/1367-2630/15/7/073011]. We find that spin oscillations may occur, depending on the parity of each soliton branch, which consequently lead to ZB oscillations of the beating dark solitons. Analytical results are corroborated by numerical simulations, illustrating the robustness of the solitons.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, M.G.; Castro, A.S. de

2009-11-15

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schroedinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and moremore » efficient problem of solving an irrational algebraic equation.« less

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space.

PubMed

Herdeiro, Carlos A R; Radu, Eugen

2016-11-25

We explicitly construct static black hole solutions to the fully nonlinear, D=4, Einstein-Maxwell-anti-de Sitter (AdS) equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast to the uniqueness results for a Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, black hole solutions in an AdS electrovacuum admit an arbitrary multipole structure.

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira, Luiz P. de, E-mail: oliveira.phys@gmail.com

The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin–Kemmer–Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff–Snyder–Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles. - Highlights: • DKP bosons in a nonminimal vector square potential are studied. • Spin zero and spin one bosons havemore » the same results. • The Schiff–Snyder–Weinberg effect is observed.« less

Matter-wave dark solitons: stochastic versus analytical results.

PubMed

Cockburn, S P; Nistazakis, H E; Horikis, T P; Kevrekidis, P G; Proukakis, N P; Frantzeskakis, D J

2010-04-30

The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as done in experiments) washes out such background fluctuations, revealing a well-defined temperature-dependent temporal growth in the oscillation amplitude. The average soliton dynamics is well captured by the simpler dissipative Gross-Pitaevskii equation, both numerically and via an analytically derived equation for the soliton center based on perturbation theory for dark solitons.

Quantum entangled dark solitons formed by ultracold atoms in optical lattices.

PubMed

Mishmash, R V; Carr, L D

2009-10-02

Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in our analysis, including von Neumann and generalized quantum entropies, quantum depletion, and the pair correlation function. We find that quantum effects cause the soliton to fill in. Moreover, soliton-soliton collisions become inelastic, in strong contrast to the predictions of mean-field theory. These features show that the lifetime and collision properties of dark solitons in optical lattices provide clear signals of quantum effects.

280  GHz dark soliton fiber laser.

PubMed

Song, Y F; Guo, J; Zhao, L M; Shen, D Y; Tang, D Y

2014-06-15

We report on an ultrahigh repetition rate dark soliton fiber laser. We show both numerically and experimentally that by taking advantage of the cavity self-induced modulation instability and the dark soliton formation in a net normal dispersion cavity fiber laser, stable ultrahigh repetition rate dark soliton trains can be formed in a dispersion-managed cavity fiber laser. Stable dark soliton trains with a repetition rate as high as ∼280  GHz have been generated in our experiment. Numerical simulations have shown that the effective gain bandwidth limitation plays an important role on the stabilization of the formed dark solitons in the laser.

Matter-wave solitons supported by quadrupole-quadrupole interactions and anisotropic discrete lattices

NASA Astrophysics Data System (ADS)

Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin

2018-04-01

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

Emission of dispersive waves from a train of dark solitons in optical fibers.

PubMed

Marest, T; Mas Arabí, C; Conforti, M; Mussot, A; Milián, C; Skryabin, D V; Kudlinski, A

2016-06-01

We report the experimental observation of multiple dispersive waves (DWs) emitted in the anomalous dispersion region of an optical fiber from a train of dark solitons. Each DW can be associated to one dark soliton of the train, using phase-matching arguments involving higher-order dispersion and soliton velocity. For a large number of dark solitons (>10), we observe the formation of a continuum associated with the efficient emission of DWs.

New Double-Periodic Soliton Solutions for the (2+1)-Dimensional Breaking Soliton Equation

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu

2018-05-01

Under investigation is the (2+1)-dimensional breaking soliton equation. Based on a special ansätz functions and the bilinear form, some entirely new double-periodic soliton solutions for the (2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures. Supported by National Natural Science Foundation of China under Grant No. 61377067

Properties of an optical soliton gas

NASA Astrophysics Data System (ADS)

Schwache, A.; Mitschke, F.

1997-06-01

We consider light pulses propagating in an optical fiber ring resonator with anomalous dispersion. New pulses are fed into the resonator in synchronism with its round-trip time. We show that solitary pulse shaping leads to a formation of an ensemble of subpulses that are identified as solitons. All solitons in the ensemble are in perpetual relative motion like molecules in a fluid; thus we refer to the ensemble as a soliton gas. Properties of this soliton gas are determined numerically.

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

Solitons for a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Xie, Xi-Yang; Chai, Han-Peng

2016-12-01

Investigation is given to a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon. Applying the double-logarithmic and rational transformations, respectively, under certain variable-coefficient constraints, we get two different types of bilinear forms: (a) Based on the first type, the bilinear Bäcklund transformation (BT) is derived, the N-soliton solutions in the Wronskian form are constructed, and the (N - 1)- and N-soliton solutions are proved to satisfy the bilinear BT; (b) Based on the second type, via the Hirota method, the one- and two-soliton solutions are obtained. Those two types of solutions are different. Graphic analysis on the two types shows that the soliton velocity depends on d(t), h(t), f(t) and R(t), the soliton amplitude is merely related to f(t), and the background depends on R(t) and f(t), where d(t), h(t), q(t) and f(t) are the dissipative, dispersive, nonuniform and line-damping coefficients, respectively, and R(t) is the external-force term. We present some types of interactions between the two solitons, including the head-on and overtaking interactions, interactions between the velocity- and amplitude-unvarying two solitons, between the velocity-varying while amplitude-unvarying two solitons and between the velocity- and amplitude-varying two solitons, as well as the interactions occurring on the constant and varying backgrounds.

Motion of discrete solitons assisted by nonlinearity management.

PubMed

Cuevas, Jesús; Malomed, Boris A; Kevrekidis, P G

2005-06-01

We demonstrate that time-periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schrödinger equation strongly facilitates creation of traveling solitons in the lattice. We predict this possibility in a semi-qualitative form analytically, and test it in direct numerical simulations. Systematic computations reveal several generic dynamical regimes, depending on the amplitude and frequency of the time modulation, and on the initial thrust which sets the soliton in motion. These regimes include irregular motion of the soliton, regular motion of a decaying one, and regular motion of a stable soliton. The motion may occur in both the straight and reverse directions, relative to the initial thrust. In the case of stable motion, extremely long simulations in a lattice with periodic boundary conditions demonstrate that the soliton keeps moving indefinitely long without any visible loss. Velocities of moving stable solitons are in good agreement with the analytical prediction, which is based on requiring a resonance between the ac drive and motion of the soliton through the periodic lattice. The generic dynamical regimes are mapped in the model's parameter space. Collisions between moving stable solitons are briefly investigated too, with a conclusion that two different outcomes are possible: elastic bounce, or bounce with mass transfer from one soliton to the other. The model can be realized experimentally in a Bose-Einstein condensate trapped in a deep optical lattice.

Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

2017-10-01

Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.

Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments.

PubMed

Kevrekidis, P G; Wang, Wenlong; Carretero-González, R; Frantzeskakis, D J

2017-06-16

Consider a lower-dimensional solitonic structure embedded in a higher-dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space, etc. By extending the Landau dynamics approach [Phys. Rev. Lett. 93, 240403 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.240403], we show that it is possible to capture the transverse dynamical modes (the "Kelvin modes") of the undulation of this "soliton filament" within the higher-dimensional space. These are the transverse stability or instability modes and are the ones potentially responsible for the breakup of the soliton into structures such as vortices, vortex rings, etc. We present the theory and case examples in 2D and 3D, corroborating the results by numerical stability and dynamical computations.

Pure-quartic solitons

PubMed Central

Blanco-Redondo, Andrea; Martijn, de Sterke C.; Sipe, J.E.; Krauss, Thomas F.; Eggleton, Benjamin J.; Husko, Chad

2016-01-01

Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers. PMID:26822758

Making beam splitters with dark soliton collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steiglitz, Ken

2010-10-15

We show with numerical simulations that for certain simple choices of parameters, the waveguides induced by colliding dark solitons in a Kerr medium yield a complete family of beam splitters for trapped linear waves, ranging from total transmission to total deflection. The way energy is transferred from one waveguide to another is similar to that of a directional coupler, but no special fabrication is required. Dark soliton beam splitters offer potential advantages over their bright soliton counterparts: Their transfer characteristics do not depend on the relative phase or speed of the colliding solitons; dark solitons are generally more robust thanmore » bright solitons; and the probe peaks at nulls of the pump, enhancing the signal-to-noise ratio for probe detection. The last factor is especially important for possible application to quantum information processing.« less

Evidence for an oscillating soliton/vortex ring by density engineering of a Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Shomroni, I.; Lahoud, E.; Levy, S.; Steinhauer, J.

2009-03-01

When two Bose-Einstein condensates collide with high collisional energy, the celebrated matter-wave interference pattern appears. For lower collisional energies, the repulsive interaction energy becomes significant, and the interference pattern evolves into an array of grey solitons. But the lowest collisional energies, producing a single pair of solitons, have not been probed so far. Here, we report on experiments using density engineering on the healing length scale to produce such a pair of solitons. We see evidence that the solitons evolve periodically between vortex rings and solitons. The stable, periodic evolution is in sharp contrast to the behaviour seen in previous experiments in which the solitons decay irreversibly into vortex rings through the so-called snake instability. The evolution can be understood in terms of conservation of mass and energy in a narrow condensate.

Dark soliton solution of Sasa-Satsuma equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohta, Y.

2010-03-08

The Sasa-Satsuma equation is a higher order nonlinear Schroedinger type equation which admits bright soliton solutions with internal freedom. We present the dark soliton solutions for the equation by using Gram type determinant. The dark solitons have no internal freedom and exist for both defocusing and focusing equations.

Uniform strongly interacting soliton gas in the frame of the Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Gelash, Andrey; Agafontsev, Dmitry

2017-04-01

The statistical properties of many soliton systems play the key role in the fundamental studies of integrable turbulence and extreme sea wave formation. It is well known that separated solitons are stable nonlinear coherent structures moving with constant velocity. After collisions with each other they restore the original shape and only acquire an additional phase shift. However, at the moment of strong nonlinear soliton interaction (i.e. when solitons are located close) the wave field are highly complicated and should be described by the theory of inverse scattering transform (IST), which allows to integrate the KdV equation, the NLSE and many other important nonlinear models. The usual approach of studying the dynamics and statistics of soliton wave field is based on relatively rarefied gas of solitons [1,2] or restricted by only two-soliton interactions [3]. From the other hand, the exceptional role of interacting solitons and similar coherent structures - breathers in the formation of rogue waves statistics was reported in several recent papers [4,5]. In this work we study the NLSE and use the most straightforward and general way to create many soliton initial condition - the exact N-soliton formulas obtained in the theory of the IST [6]. We propose the recursive numerical scheme for Zakharov-Mikhailov variant of the dressing method [7,8] and discuss its stability with respect to increasing the number of solitons. We show that the pivoting, i.e. the finding of an appropriate order for recursive operations, has a significant impact on the numerical accuracy. We use the developed scheme to generate statistical ensembles of 32 strongly interacting solitons, i.e. solve the inverse scattering problem for the high number of discrete eigenvalues. Then we use this ensembles as initial conditions for numerical simulations in the box with periodic boundary conditions and study statics of obtained uniform strongly interacting gas of NLSE solitons. Author thanks the support of the Russian Science Foundation (Grand No. 14-22-00174) [1] D. Dutykh, E. Pelinovsky, Numerical simulation of a solitonic gas in kdv and kdv-bbm equations, Physics Letters A 378 (42) (2014) 3102-3110. [2] E. Shurgalina, E. Pelinovsky, Nonlinear dynamics of a soliton gas: Modified korteweg-de vries equation framework, Physics Letters A 380 (24) (2016) 2049-2053. [3] E. N. Pelinovsky, E. Shurgalina, A. Sergeeva, T. G. Talipova, G. El, R. H. Grimshaw, Two-soliton interaction as an elementary act of soliton turbulence in integrable systems, Physics Letters A 377 (3) (2013) 272-275 [4] J. Soto-Crespo, N. Devine, N. Akhmediev, Integrable turbulence and rogue waves: Breathers or solitons?, Physical review letters 116 (10) (2016) 103901. [5] D. S. Agafontsev, V. E. Zakharov, Integrable turbulence and formation of rogue waves, Nonlinearity 28 (8) (2015) 2791. [6] V. E. Zakharov, A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP 34 (1) (1972) 62. [7] V. Zakharov, A. Mikhailov, Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Sov. Phys.-JETP (Engl. Transl.) 47 (6) (1978). [8] A. A. Gelash, V. E. Zakharov, Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability, Nonlinearity 27 (4) (2014) R1.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.

PubMed

Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M

2014-01-01

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Derivation of the Effective Nonlinear Schrodinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing

DTIC Science & Technology

2011-03-01

An e?ective Nonlinear Schr?dinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a... soliton amplitude profiles are displayed as a hyperbolic secant function and hold there profile at short distances on the order of centimeters. Dark ...spatial solitons are similar but have hyperbolic tangent type profiles. Dark spatial solitons were first observed by Jerominek in 1985 and Belanger and

Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation

DTIC Science & Technology

2014-12-01

dark solitons ) and vortices. Early soliton experiments of about 15 years ago observed the motion of a dark soliton towards the edge of the trap [27...of dark soliton oscillations in a unitary Fermi gas [30]. A number of the- oretical studies have provided relevant explanation for this phenomenology...in atomic BECs [31, 32, 33, 34, 35, 36, 37, 38, 39]. In particular, it has been identified in these works that the dark soliton follows an anti

Probe-controlled soliton frequency shift in the regime of optical event horizon.

PubMed

Gu, Jie; Guo, Hairun; Wang, Shaofei; Zeng, Xianglong

2015-08-24

In optical analogy of the event horizon, temporal pulse collision and mutual interactions are mainly between an intense solitary wave (soliton) and a dispersive probe wave. In such a regime, here we numerically investigate the probe-controlled soliton frequency shift as well as the soliton self-compression. In particular, in the dispersion landscape with multiple zero dispersion wavelengths, bi-directional soliton spectral tunneling effects is possible. Moreover, we propose a mid-infrared soliton self-compression to the generation of few-cycle ultrashort pulses, in a bulk of quadratic nonlinear crystals in contrast to optical fibers or cubic nonlinear media, which could contribute to the community with a simple and flexible method to experimental implementations.

Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser.

PubMed

Liu, Meng; Luo, Ai-Ping; Xu, Wen-Cheng; Luo, Zhi-Chao

2016-09-01

We reported on the observation of dissipative rogue waves (DRWs) induced by soliton explosions in an ultrafast fiber laser. It was found that the soliton explosions could be obtained in the fiber laser at a critical pump power level. During the process of the soliton explosion, the high-amplitude waves that fulfill the rogue wave criteria could be detected. The appearance of the DRWs was identified by characterizing the intensity statistics of the time-stretched soliton profile based on the dispersive Fourier-transform method. Our findings provide the first experimental demonstration that the DRWs could be observed in the soliton explosion regime and further enhance the understanding of the physical mechanism of optical RW generation.

Interaction of spatially separated oscillating solitons in biased two-photon photorefractive materials

NASA Astrophysics Data System (ADS)

Asif, Noushin; Biswas, Anjan; Jovanoski, Z.; Konar, S.

2015-01-01

This paper presents the dynamics of two spatially separated optical solitons in two-photon photorefractive materials. The variational formalism has been employed to derive evolution equations of different parameters which characterize the dynamics of two interacting solitons. This approach yields a system of coupled ordinary differential equations for evolution of different parameters characterizing solitons such as amplitude, spatial width, chirp, center of gravity, etc., which have been subsequently solved adopting numerical method to extract information on their dynamics. Depending on their initial separation and power, solitons are shown to either disperse or compresses individually and attract each other. Dragging and trapping of a probe soliton by another pump have been discussed.

N-Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation

NASA Astrophysics Data System (ADS)

Wang, Xin; Geng, Xian-Guo

2017-08-01

We derive the Lax pair and Darboux transformation for the (2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlevé analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively. Supported by National Natural Science Foundation of China under Grant No. 11331008 and China Postdoctoral Science Foundation Funded Sixtieth Batches (2016M602252)

One-dimensional spatial dark soliton-induced channel waveguides in lithium niobate crystal.

PubMed

Zhang, Peng; Ma, Yanghua; Zhao, Jianlin; Yang, Dexing; Xu, Honglai

2006-04-01

The anisotropic dependence of the formation of one-dimensional (1-D) spatial dark solitons on the orientation of intensity gradients in lithium niobate crystal is numerically specified. Based on this, we propose an approach to fabricate channel waveguides by employing 1-D spatial dark solitons. By exposure of two 1-D dark solitons with different orientations, channel waveguides can be created. The structures of the channel waveguides can be tuned by adjustment of the widths of the solitons and/or the angles between the two exposures. A square channel waveguide is experimentally demonstrated in an iron-doped lithium niobate crystal by exposure of two orthogonal 1-D dark solitons in sequence.

First Observation of Bright Solitons in Bulk Superfluid ^{4}He.

PubMed

Ancilotto, Francesco; Levy, David; Pimentel, Jessica; Eloranta, Jussi

2018-01-19

The existence of bright solitons in bulk superfluid ^{4}He is demonstrated by time-resolved shadowgraph imaging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of nonlinear waves is produced by rapidly expanding plasma from laser ablation. After the leading dissipative period, these waves transform into bright solitons, which exhibit three characteristic features: dispersionless propagation, negligible interaction in a two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supported by DFT calculations, which show rapid evolution of the initially compressed liquid into bright solitons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.

Bäcklund transformation and soliton solutions in terms of the Wronskian for the Kadomtsev-Petviashvili-based system in fluid dynamics

NASA Astrophysics Data System (ADS)

Du, Zhong; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Wu, Xiao-Yu

2018-04-01

In this paper, investigation is made on a Kadomtsev-Petviashvili-based system, which can be seen in fluid dynamics, biology and plasma physics. Based on the Hirota method, bilinear form and Bäcklund transformation (BT) are derived. N-soliton solutions in terms of the Wronskian are constructed, and it can be verified that the N-soliton solutions in terms of the Wronskian satisfy the bilinear form and Bäcklund transformation. Through the N-soliton solutions in terms of the Wronskian, we graphically obtain the kink-dark-like solitons and parallel solitons, which keep their shapes and velocities unchanged during the propagation.

Black and gray Helmholtz-Kerr soliton refraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.

Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposalmore » of positive or negative lensing operations on soliton arrays at planar boundaries.« less

You can hide but you have to run: direct detection with vector mediators

NASA Astrophysics Data System (ADS)

D'Eramo, Francesco; Kavanagh, Bradley J.; Panci, Paolo

2016-08-01

We study direct detection in simplified models of Dark Matter (DM) in which interactions with Standard Model (SM) fermions are mediated by a heavy vector boson. We consider fully general, gauge-invariant couplings between the SM, the mediator and both scalar and fermion DM. We account for the evolution of the couplings between the energy scale of the mediator mass and the nuclear energy scale. This running arises from virtual effects of SM particles and its inclusion is not optional. We compare bounds on the mediator mass from direct detection experiments with and without accounting for the running. In some cases the inclusion of these effects changes the bounds by several orders of magnitude, as a consequence of operator mixing which generates new interactions at low energy. We also highlight the importance of these effects when translating LHC limits on the mediator mass into bounds on the direct detection cross section. For an axial-vector mediator, the running can alter the derived bounds on the spin-dependent DM-nucleon cross section by a factor of two or more. Finally, we provide tools to facilitate the inclusion of these effects in future studies: general approximate expressions for the low energy couplings and a public code runDM to evolve the couplings between arbitrary energy scales.

Charm-beauty meson bound states from B (B*)D (D*) and B (B*)D \\xAF(D\\xAF*) interaction

NASA Astrophysics Data System (ADS)

Sakai, S.; Roca, L.; Oset, E.

2017-09-01

We evaluate the s -wave interaction of pseudoscalar and vector mesons with both charm and beauty to investigate the possible existence of molecular B D , B*D , B D*, B*D*, B D ¯, B*D ¯, B D¯*, or B*D¯* meson states. The scattering amplitude is obtained implementing unitarity starting from a tree level potential accounting for the dominant vector meson exchange. The diagrams are evaluated using suitable extensions to the heavy flavor sector of the hidden gauge symmetry Lagrangians involving vector and pseudoscalar mesons, respecting heavy quark spin symmetry. We obtain bound states at energies above 7 GeV for B D (JP=0+), B*D (1+), B D* (1+), and B*D* (0+, 1+, 2+), all in isospin 0. For B D ¯ (0+), B*D ¯ (1+), B D¯* (1+), and B*D¯* (0+, 1+, 2+) we also find similar bound states in I =0 , but much less bound, which would correspond to exotic meson states with b ¯ and c ¯ quarks, and for the I =1 we find a repulsive interaction. We also evaluate the scattering lengths in all cases, which can be tested in current investigations of lattice QCD.

Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma

NASA Astrophysics Data System (ADS)

Wang, Yong-Yan; Su, Chuan-Qi; Liu, Xue-Qing; Li, Jian-Guang

2018-07-01

Under investigation in this paper is an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma. Lax pair, bilinear forms, and bilinear Bäcklund transformations are derived. Based on the bilinear forms, the first-, second-, and third-order nonautonomous soliton solutions are derived. Propagation and interaction of the nonautonomous solitons are investigated and influence of the variable coefficients is also discussed: Amplitude of the first-order nonautonomous soliton is determined by the spectral parameter and perturbed factor; there exist two kinds of the solitons, namely the elevation and depression solitons, depending on the sign of the spectral parameter; the background where the nonautonomous soliton exists is influenced by the perturbed factor and external force coefficient; breather solutions can be constructed under the conjugate condition, and period of the breather is related to the dispersive and nonuniform coefficients.

Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Wei, Yuan; Li, Bowen; Wei, Xiaoming; Yu, Ying; Wong, Kenneth K. Y.

2018-02-01

The single-shot spectral dynamics of dual-color-soliton collisions inside a mode-locked laser is experimentally and numerically investigated. By using the all-optically dispersive Fourier transform, we spectrally unveil the collision-induced soliton self-reshaping process, which features dynamic spectral fringes over the soliton main lobe, and the rebuilding of Kelly sidebands with wavelength drifting. Meanwhile, the numerical simulations validate the experimental observation and provide additional insights into the physical mechanism of the collision-induced spectral dynamics from the temporal domain perspective. It is verified that the dynamic interference between the soliton and the dispersive waves is responsible for the observed collision-induced spectral evolution. These dynamic phenomena not only demonstrate the role of dispersive waves in the sophisticated soliton interaction inside the laser cavity, but also facilitate a deeper understanding of the soliton's inherent stability.

Boundary enhanced effects on the existence of quadratic solitons

NASA Astrophysics Data System (ADS)

Chen, Manna; Zhang, Ting; Li, Wenjie; Lu, Daquan; Guo, Qi; Hu, Wei

2018-05-01

We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell's strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential.

PubMed

Li, Min; Xu, Tao

2015-03-01

Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.

Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang

2017-04-01

Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.

Experimental observation of different soliton types in a net-normal group-dispersion fiber laser.

PubMed

Feng, Zhongyao; Rong, Qiangzhou; Qiao, Xueguang; Shao, Zhihua; Su, Dan

2014-09-20

Different soliton types are observed in a net-normal group-dispersion fiber laser based on nonlinear polarization rotation for passive mode locking. The proposed laser can deliver a dispersion-managed soliton, typical dissipation solitons, and a quasi-harmonic mode-locked pulse, a soliton bundle, and especially a dark pulse by only appropriately adjusting the linear cavity phase delay bias using one polarization controller at the fixed pump power. These nonlinear waves show different features, including the spectral shapes and time traces. The experimental observations show that the five soliton types could exist in the same laser cavity, which implies that integrable systems, dissipative systems, and dark pulse regimes can transfer and be switched in a passively mode-locked laser. Our studies not only verify the numeral simulation of the different soliton-types formation in a net-normal group-dispersion operation but also provide insight into Ginzburg-Landau equation systems.

Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law

PubMed Central

Biktashev, V. N.; Tsyganov, M. A.

2016-01-01

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, “excitable” systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems. PMID:27491430

A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2018-04-01

We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

Soliton wave-speed management: Slowing, stopping, or reversing a solitary wave

NASA Astrophysics Data System (ADS)

Baines, Luke W. S.; Van Gorder, Robert A.

2018-06-01

While dispersion management is a well-known tool to control soliton properties such as shape or amplitude, far less effort has been directed toward the theoretical control of the soliton wave speed. However, recent experiments concerning the stopping or slowing of light demonstrate that the control of the soliton wave speed is of experimental interest. Motivated by these and other studies, we propose a management approach for modifying the wave speed of a soliton (or of other nonlinear wave solutions, such as periodic cnoidal waves) under the nonlinear Schrödinger equation. Making use of this approach, we are able to slow, stop, or even reverse a solitary wave, and we give several examples to bright solitons, dark solitons, and periodic wave trains, to demonstrate the method. An extension of the approach to spatially heterogeneous media, for which the wave may propagate differently at different spatial locations, is also discussed.

Density engineering of an oscillating soliton/vortex ring in a Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Levy, Shahar; Shomroni, Itay; Lahoud, Elias; Steinhauer, Jeff

2008-05-01

We study solitons in a Bose-Einstein condensate by engineering a density minimum on the healing length scale, using a far off-resonant laser beam. This results in a pair of counterpropagating solitons, which is the low collisional energy version of the celebrated matter wave interference pattern [M. R. Andrews et al., Science 275, 637 (1997)]. The solitons subsequently evolve into a pair of periodic soliton/vortex rings. We image the vortex rings and solitons in-situ on the healing length scale. This stable periodic evolution is in sharp contrast to the behavior of previous experiments in which the solitons decay irreversibly into vortex rings via the snake instability. The periodic oscillation between two qualitatively different forms seems to be a rare phenomenon in nature. We explain this phenomenon in terms of conservation of mass and energy in a narrow condensate.

Controlling formation and suppression of fiber-optical rogue waves.

PubMed

Brée, Carsten; Steinmeyer, Günter; Babushkin, Ihar; Morgner, Uwe; Demircan, Ayhan

2016-08-01

Fiber-optical rogue waves appear as rare but extreme events during optical supercontinuum generation in photonic crystal fibers. This process is typically initiated by the decay of a high-order fundamental soliton into fundamental solitons. Collisions between these solitons as well as with dispersive radiation affect the soliton trajectory in frequency and time upon further propagation. Launching an additional dispersive wave at carefully chosen delay and wavelength enables statistical manipulation of the soliton trajectory in such a way that the probability of rogue wave formation is either enhanced or reduced. To enable efficient control, parameters of the dispersive wave have to be chosen to allow trapping of dispersive radiation in the nonlinear index depression created by the soliton. Under certain conditions, direct manipulation of soliton properties is possible by the dispersive wave. In other more complex scenarios, control is possible via increasing or decreasing the number of intersoliton collisions. The control mechanism reaches a remarkable efficiency, enabling control of relatively large soliton energies. This scenario appears promising for highly dynamic all-optical control of supercontinua.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Soliton formation from a noise-like pulse during extreme events in a fibre ring laser

NASA Astrophysics Data System (ADS)

Pottiez, O.; Ibarra-Villalon, H. E.; Bracamontes-Rodriguez, Y.; Minguela-Gallardo, J. A.; Garcia-Sanchez, E.; Lauterio-Cruz, J. P.; Hernandez-Garcia, J. C.; Bello-Jimenez, M.; Kuzin, E. A.

2017-10-01

We study experimentally the interactions between soliton and noise-like pulse (NLP) components in a mode-locked fibre ring laser operating in a hybrid soliton-NLP regime. For proper polarization adjustments, one NLP and multiple packets of solitons coexist in the cavity, at 1530 nm and 1558 nm, respectively. By examining time-domain sequences measured using a 16 GHz real-time oscilloscope, we unveil the process of soliton genesis: they are produced during extreme-intensity episodes affecting the NLP. These extreme events can emerge sporadically, appear in small groups or even form quasi-periodic sequences. Once formed, the wavelength-shifted soliton packet drifts away from the NLP in the dispersive cavity, and eventually vanishes after a variable lifetime. Evidence of the inverse process, through which NLP formation is occasionally seeded by an extreme-intensity event affecting a bunch of solitons, is also provided. The quasi-stationary dynamics described here constitutes an impressive illustration of the connections and interactions between NLPs, extreme events and solitons in passively mode-locked fibre lasers.

Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system.

PubMed

Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

2018-01-01

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N ( N ≥2) lumps annihilating into or producing from N -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

2018-01-01

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N(N≥2) lumps annihilating into or producing from N-dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun

2018-02-01

We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakaguchi, Hidetsugu; Malomed, Boris A.

We study ordinary solitons and gap solitons (GS's) in the framework of the one-dimensional Gross-Pitaevskii equation (GPE) with a combination of both linear and nonlinear lattice potentials. The main points of the analysis are the effects of (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons and various forms of the averaging method for broad solitons of both types, and also the study of the mobility of the solitons. Under the direct commensurability (equal periods of the lattices, L{sub lin}=L{sub nonlin}), the family of ordinary solitons is similar to its counterpartmore » in the GPE without external potentials. In the case of the subharmonic commensurability with L{sub lin}=(1/2)L{sub nonlin}, or incommensurability, there is an existence threshold for the ordinary solitons and the scaling relation between their amplitude and width is different from that in the absence of the potentials. GS families demonstrate a bistability unless the direct commensurability takes place. Specific scaling relations are found for them as well. Ordinary solitons can be readily set in motion by kicking. GS's are also mobile and feature inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the Vakhitov-Kolokolov (VK) criterion (i.e., a negative slope in the dependence between the solitons's chemical potential mu and norm N). The stability of GS families obeys an inverted ('anti-VK') criterion dmu/dN>0, which is explained by the approximation based on the averaging method. The present system provides for the unique possibility to check the anti-VK criterion, as mu(N) dependencies for GS's feature turning points except in the case of direct commensurability.« less

Coupled matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Golam Ali, Sk; Talukdar, B.

2009-06-01

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (Veff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well Veff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of Veff(LOL) increases as k increases and that of Veff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.

The laboratory investigation of surface envelope solitons: reflection from a vertical wall and collisions of solitons

NASA Astrophysics Data System (ADS)

Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.

2016-04-01

Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105 (2013). [2] A.I. Dyachenko, V.E. Zakharov, On the formation of freak waves on the surface of deep water. JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676 (2009).

Magnetic moments of the lowest-lying singly heavy baryons

NASA Astrophysics Data System (ADS)

Yang, Ghil-Seok; Kim, Hyun-Chul

2018-06-01

A light baryon is viewed as Nc valence quarks bound by meson mean fields in the large Nc limit. In much the same way a singly heavy baryon is regarded as Nc - 1 valence quarks bound by the same mean fields, which makes it possible to use the properties of light baryons to investigate those of the heavy baryons. A heavy quark being regarded as a static color source in the limit of the infinitely heavy quark mass, the magnetic moments of the heavy baryon are determined entirely by the chiral soliton consisting of a light-quark pair. The magnetic moments of the baryon sextet are obtained by using the parameters fixed in the light-baryon sector. In this mean-field approach, the numerical results of the magnetic moments of the baryon sextet with spin 3/2 are just 3/2 larger than those with spin 1/2. The magnetic moments of the bottom baryons are the same as those of the corresponding charmed baryons.

The Eccentric Behavior of Nearly Frozen Orbits

NASA Technical Reports Server (NTRS)

Sweetser, Theodore H.; Vincent, Mark A.

2013-01-01

Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose eccentricity and argument of periapse have values close to those of a frozen orbit. We call them "nearly" frozen because their eccentricity vector (a vector whose polar coordinates are eccentricity and argument of periapse) will stay within a bounded distance from the frozen orbit eccentricity vector, circulating around it over time. For highly inclined orbits around the Earth, this distance is effectively constant over time. Furthermore, frozen orbit eccentricity values are low enough that these orbits are essentially eccentric (i.e., off center) circles, so that nearly frozen orbits around Earth are bounded above and below by frozen orbits.

Soliton resonance in bose-einstein condensate

NASA Technical Reports Server (NTRS)

Zak, Michail; Kulikov, I.

2002-01-01

A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.

Soliton all-optical logic AND gate with semiconductor optical amplifier-assisted Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Kotb, Amer; Zoiros, Kyriakos E.

2016-08-01

The concept of soliton provides a line in research in telecommunications systems. In the present study, a soliton all-optical logic AND gate with semiconductor optical amplifier (SOA)-assisted Mach-Zehnder interferometer has been numerically simulated and investigated. The dependence of the output quality factor (Q-factor) on the soliton characteristics and SOA parameters has been examined and assessed. The obtained results demonstrate that the soliton AND gate is capable of operating at a data rate of 80 Gb/s with logical correctness and high-output Q-factor.

Generation of dark solitons in erbium-doped fiber lasers based Sb(2)Te(3) saturable absorbers.

PubMed

Liu, Wenjun; Pang, Lihui; Han, Hainian; Tian, Wenlong; Chen, Hao; Lei, Ming; Yan, Peiguang; Wei, Zhiyi

2015-10-05

Dark solitons, which have better stability in the presence of noise, have potential applications in optical communication and ultrafast optics. In this paper, the dark soliton formation in erbium-doped fiber lasers based Sb(2)Te(3) saturable absorber (SA) is first experimentally demonstrated. The Sb(2)Te(3) SA is fabricated by using the pulsed laser deposition method. The generated dark solitons are centered at the wavelength of 1530 nm and repetition rate of 94 MHz. Analytic solutions for dark solitons are also obtained theoretically.

Optical solitons to the resonance nonlinear Schrödinger equation by Sine-Gordon equation method

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2018-01-01

In this paper, we examined the optical solitons to the resonant nonlinear Schrödinger equation (R-NLSE) which describes the propagation of solitons through optical fibers. Three types of nonlinear media fibers are studied. They are; quadratic-cubic law, Kerr law and parabolic law. Dark, bright, dark-bright or combined optical and singular soliton solutions are derived using the sine-Gordon equation method (SGEM). The constraint conditions that naturally fall out of the solution structure which guarantee the existence of these solitons are also reported.

Multiple periodic-soliton solutions of the (3+1)-dimensional generalised shallow water equation

NASA Astrophysics Data System (ADS)

Li, Ye-Zhou; Liu, Jian-Guo

2018-06-01

Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3 {+} 1)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.

Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations.

PubMed

Chowdury, Amdad; Krolikowski, Wieslaw

2017-06-01

We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.

Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Meidan; Li, Biao

2017-11-01

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2+1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.

Few-cycle solitons and supercontinuum generation with cascaded quadratic nonlinearities in unpoled lithium niobate ridge waveguides.

PubMed

Guo, Hairun; Zeng, Xianglong; Zhou, Binbin; Bache, Morten

2014-03-01

Formation and interaction of few-cycle solitons in a lithium niobate ridge waveguide are numerically investigated. The solitons are created through a cascaded phase-mismatched second-harmonic generation process, which induces a dominant self-defocusing Kerr-like nonlinearity on the pump pulse. The inherent material self-focusing Kerr nonlinearity is overcome over a wide wavelength range, and self-defocusing solitons are supported from 1100 to 1900 nm, covering the whole communication band. Single cycle self-compressed solitons and supercontinuum generation spanning 1.3 octaves are observed when pumped with femtosecond nanojoule pulses at 1550 nm. The waveguide is not periodically poled, as quasi-phase-matching would lead to detrimental nonlinear effects impeding few-cycle soliton formation.

Dark soliton decay due to trap anharmonicity in atomic Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parker, N. G.; Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1; School of Food Science and Nutrition, University of Leeds, Leeds LS2 9JT

2010-03-15

A number of recent experiments with nearly pure atomic Bose-Einstein condensates have confirmed the predicted dark soliton oscillations when under harmonic trapping. However, a dark soliton propagating in an inhomogeneous condensate has also been predicted to be unstable to the emission of sound waves. Although harmonic trapping supports an equilibrium between the coexisting soliton and sound, we show that the ensuing dynamics are sensitive to trap anharmonicities. Such anharmonicities can break the soliton-sound equilibrium and lead to the net decay of the soliton on a considerably shorter time scale than other dissipation mechanisms. Thus, we propose that small realistic modificationsmore » to existing experimental setups could enable the experimental observation of this decay channel.« less

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg Landau equation with variable coefficients

NASA Astrophysics Data System (ADS)

Fang, Fang; Xiao, Yan

2006-12-01

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.

Harnessing energy-sharing collisions of Manakov solitons to implement universal NOR and OR logic gates

NASA Astrophysics Data System (ADS)

Vijayajayanthi, M.; Kanna, T.; Murali, K.; Lakshmanan, M.

2018-06-01

The energy-sharing collision of bright optical solitons in the Manakov system, governing pulse propagation in high birefringent fiber, is employed theoretically to realize optical logic gates. In particular, we successfully construct (theoretically) the universal NOR gate and the OR gate from the energy-sharing collisions of just four bright solitons which can be well described by the exact bright four-soliton solution of the Manakov system. This construction procedure has important merits such as realizing the two input gates with a minimal number of soliton collisions and possibilities of multistate logic. The recent experiments on Manakov solitons suggest the possibility of implementation of this theoretical construction of such gates and ultimately an all-optical computer.

Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains

NASA Astrophysics Data System (ADS)

Koulouri, Alexandra; Brookes, Mike; Rimpiläinen, Ville

2017-01-01

In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field.

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zajnulina, M.; Giannone, D.; Haynes, R.

We propose a fibre-based approach for generation of optical frequency combs (OFCs) with the aim of calibration of astronomical spectrographs in the low and medium-resolution range. This approach includes two steps: in the first step, an appropriate state of optical pulses is generated and subsequently moulded in the second step delivering the desired OFC. More precisely, the first step is realised by injection of two continuous-wave (CW) lasers into a conventional single-mode fibre, whereas the second step generates a broad OFC by using the optical solitons generated in step one as initial condition. We investigate the conversion of a bichromaticmore » input wave produced by two initial CW lasers into a train of optical solitons, which happens in the fibre used as step one. Especially, we are interested in the soliton content of the pulses created in this fibre. For that, we study different initial conditions (a single cosine-hump, an Akhmediev breather, and a deeply modulated bichromatic wave) by means of soliton radiation beat analysis and compare the results to draw conclusion about the soliton content of the state generated in the first step. In case of a deeply modulated bichromatic wave, we observed the formation of a collective soliton crystal for low input powers and the appearance of separated solitons for high input powers. An intermediate state showing the features of both, the soliton crystal and the separated solitons, turned out to be most suitable for the generation of OFC for the purpose of calibration of astronomical spectrographs.« less

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers.

PubMed

Zajnulina, M; Böhm, M; Blow, K; Rieznik, A A; Giannone, D; Haynes, R; Roth, M M

2015-10-01

We propose a fibre-based approach for generation of optical frequency combs (OFCs) with the aim of calibration of astronomical spectrographs in the low and medium-resolution range. This approach includes two steps: in the first step, an appropriate state of optical pulses is generated and subsequently moulded in the second step delivering the desired OFC. More precisely, the first step is realised by injection of two continuous-wave (CW) lasers into a conventional single-mode fibre, whereas the second step generates a broad OFC by using the optical solitons generated in step one as initial condition. We investigate the conversion of a bichromatic input wave produced by two initial CW lasers into a train of optical solitons, which happens in the fibre used as step one. Especially, we are interested in the soliton content of the pulses created in this fibre. For that, we study different initial conditions (a single cosine-hump, an Akhmediev breather, and a deeply modulated bichromatic wave) by means of soliton radiation beat analysis and compare the results to draw conclusion about the soliton content of the state generated in the first step. In case of a deeply modulated bichromatic wave, we observed the formation of a collective soliton crystal for low input powers and the appearance of separated solitons for high input powers. An intermediate state showing the features of both, the soliton crystal and the separated solitons, turned out to be most suitable for the generation of OFC for the purpose of calibration of astronomical spectrographs.

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

NASA Astrophysics Data System (ADS)

Zajnulina, M.; Böhm, M.; Blow, K.; Rieznik, A. A.; Giannone, D.; Haynes, R.; Roth, M. M.

2015-10-01

We propose a fibre-based approach for generation of optical frequency combs (OFCs) with the aim of calibration of astronomical spectrographs in the low and medium-resolution range. This approach includes two steps: in the first step, an appropriate state of optical pulses is generated and subsequently moulded in the second step delivering the desired OFC. More precisely, the first step is realised by injection of two continuous-wave (CW) lasers into a conventional single-mode fibre, whereas the second step generates a broad OFC by using the optical solitons generated in step one as initial condition. We investigate the conversion of a bichromatic input wave produced by two initial CW lasers into a train of optical solitons, which happens in the fibre used as step one. Especially, we are interested in the soliton content of the pulses created in this fibre. For that, we study different initial conditions (a single cosine-hump, an Akhmediev breather, and a deeply modulated bichromatic wave) by means of soliton radiation beat analysis and compare the results to draw conclusion about the soliton content of the state generated in the first step. In case of a deeply modulated bichromatic wave, we observed the formation of a collective soliton crystal for low input powers and the appearance of separated solitons for high input powers. An intermediate state showing the features of both, the soliton crystal and the separated solitons, turned out to be most suitable for the generation of OFC for the purpose of calibration of astronomical spectrographs.

Solitonic properties for a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Qu, Qi-Xing; Zhen, Hui-Ling; Chai, Han-Peng

2018-07-01

In this paper, investigation is given to a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon. Based on the Lax pair, under certain variable-coefficient-dependent constraints, we present an infinite sequence of the conservation laws. Through the Riccati equations obtained from the Lax pair, a Wahlquist-Estabrook-type Bäcklund transformation (BT) is derived, based on which the nonlinear superposition formula as well as one- and two-soliton-like solutions are obtained. Via the truncated Painlevé expansion, we give a Painlevé BT, along with the one-soliton-like solutions. With the Painlevé BT, bilinear forms are constructed, and we get a bilinear BT as well as the corresponding one-soliton-like solutions. Bell-type bright and dark soliton-like waves and kink-type soliton-like waves are observed, respectively. Graphic analysis shows that (1) the velocities of the soliton-like waves are related to h(t), d(t), f(t) and R(t), while the soliton-like wave amplitudes just depend on f(t), and (2) with the nonzero f(t) and R(t), soliton-like waves propagate on the varying backgrounds, where h(t), d(t) and f(t) are the dispersive, dissipative and line-damping coefficients, respectively, R(t) is the external-force term, and t is the scaled time coordinate.

Neutron scattering on solitons in quasi-one-dimensional systems

NASA Astrophysics Data System (ADS)

Fedyanin, V. K.

1983-05-01

In the framework of the model of an ideal lattice gas of solitons, we obtain the following general formula for the dynamic neutron scattering form factor: S(q, w) = N¯S 1(q, w) , S(q, w) = {p‧(ν 0)δ 22}/{2πqZ 1h }f 2(qδ(ν 0 Here q = k‧ - k and w = E‧ - E are the neutron momentum and energy transfer, respectively, ν0 = wq-1, δ(ν) is the soliton width of velocity ν, p‧( ν0) = d p/d ν| ν0 , p(ν) is the soliton momentum, E(p(ν)) is the soliton energy, N¯ is the average number of solitons at θ = kδT = β-1 and is constructed from the soliton non-linear differential equations. The derivation of the formula is essentially based on (i) specific dependence of these solutions on ξ = x - vt, and (ii) generalization of the averaging over the soliton ensemble, proposed in ref. [1]. The specifi properties of the scattering spectra of polypeptides, DNA molecules and magnetics as functions of the temperature and interaction parameters and of external fields are discussed on the basis of this formula. The contribution to S(q, w) for “slow” solitons in magnetics has been calculated in [2, 3]. (For each concrete model the authors were forced to formulate anew the way of calculation, to assume the small size of ν, etc.)

Soliton Resolution for the Derivative Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine

2018-05-01

We study the derivative nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou (Commun Pure Appl Math 56:1029-1077, 2003) revisited by the {\\overline{partial}} -analysis of McLaughlin and Miller (IMRP Int Math Res Pap 48673:1-77, 2006) and Dieng and McLaughlin (Long-time asymptotics for the NLS equation via dbar methods. Preprint, arXiv:0805.2807, 2008), and complemented by the recent work of Borghese et al. (Ann Inst Henri Poincaré Anal Non Linéaire, https://doi.org/10.1016/j.anihpc.2017.08.006, 2017) on soliton resolution for the focusing nonlinear Schrödinger equation. Our results imply that N-soliton solutions of the derivative nonlinear Schrödinger equation are asymptotically stable.

Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions

NASA Astrophysics Data System (ADS)

El-Wakil, S. A.; Abulwafa, Essam M.; Elhanbaly, Atalla A.

2017-07-01

Based on Sagdeev pseudo-potential and phase-portrait, the dynamics of four-component dust plasma with non-extensively distributed electrons and ions are investigated. Three distinct types of nonlinear waves, namely, soliton, double layer, and super-soliton, have been found. The basic features of such waves are high sensitivity to Mach number, non-extensive parameter, and dust temperature ratio. It is found that the multi-component plasma is a necessary condition for super-soliton's existence, having a wider amplitude and a larger width than the regular soliton. Super-solitons may also exist when the Sagdeev pseudo-potential curves admit at least four extrema and two roots. In our multi-component plasma system, the super-solitons can be found by increasing the Mach number and the non-extensive parameter beyond those of double-layers. On the contrary, the super-soliton can be produced by decreasing the dust temperature ratio. The conditions of the onset of such nonlinear waves and its merging to regular solitons have been studied. This work shows that the obtained nonlinear waves are found to exist only in the super-sonic Mach number regime. The obtained results may be of wide relevance in the field of space plasma and may also be helpful to better understand the nonlinear fluctuations in the Auroral-zone of the Earth's magnetosphere.

A new class of non-topological solitons

NASA Technical Reports Server (NTRS)

Frieman, Joshua A.; Lynn, Bryan W.

1989-01-01

A class of non-topological solitons was constructed in renormalizable scalar field theories with nonlinear self-interactions. For large charge Q, the soliton mass increases linearly with Q, i.e., the soliton mass density is approximately independent of charge. Such objects could be naturally produced in a phase transition in the early universe or in the decay of superconducting cosmic strings.

Noncommuting Momenta of Topological Solitons

NASA Astrophysics Data System (ADS)

Watanabe, Haruki; Murayama, Hitoshi

2014-05-01

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids

NASA Astrophysics Data System (ADS)

Ackerman, Paul J.; Smalyukh, Ivan I.

2017-04-01

Three-dimensional (3D) topological solitons are continuous but topologically nontrivial field configurations localized in 3D space and embedded in a uniform far-field background, that behave like particles and cannot be transformed to a uniform state through smooth deformations. Many topologically nontrivial 3D solitonic fields have been proposed. Yet, according to the Hobart-Derrick theorem, physical systems cannot host them, except for nonlinear theories with higher-order derivatives such as the Skyrme-Faddeev model. Experimental discovery of such solitons is hindered by the need for spatial imaging of the 3D fields, which is difficult in high-energy physics and cosmology. Here we experimentally realize and numerically model stationary topological solitons in a fluid chiral ferromagnet formed by colloidal dispersions of magnetic nanoplates. Such solitons have closed-loop preimages--3D regions with a single orientation of the magnetization field. We discuss localized structures with different linking of preimages quantified by topological Hopf invariants. The chirality is found to help in overcoming the constraints of the Hobart-Derrick theorem, like in two-dimensional ferromagnetic solitons, dubbed `baby skyrmions'. Our experimental platform may lead to solitonic condensed matter phases and technological applications.

Dual noise-like pulse and soliton operation of a fiber ring cavity

NASA Astrophysics Data System (ADS)

Bracamontes Rodríguez, Y. E.; Pottiez, O.; García Sanchez, E.; Lauterio Cruz, J. P.; Ibarra-Villalón, H.; Hernandez-Garcia, J. C.; Bello-Jimenez, M.; Beltrán-Pérez, G.; Ibarra-Escamilla, B.; Kuzin, E. A.

2017-03-01

Passively mode-locked fiber lasers (PML-FLs) are versatile sources that are capable of generating a broad variety of short and ultrashort optical pulses. Besides conservative solitons, PML-FLs allow the generation of different kinds of dissipative structures, usually called dissipative solitons, a concept that also encompasses more complex structures and collective behaviors such as soliton molecules, gas, rain of solitons, etc. In addition to this, PML-FLs are also able to generate even more complex objects, the so-called noise-like pulses (NLPs). A few recent research results revealed a connection between NLPs and solitons, a sign that deterministic ingredients enter into the composition of NLPs, whose nature is traditionally assumed to be random. Although it is usual that a fiber laser is able to generate either solitons or noise-like pulses, depending on pump power and adjustments in the cavity, these two regimes are rarely observed simultaneously. In this paper, a PML-FL in a ring configuration is presented, in which it is possible to observe and verify experimentally the simultaneous presence of NLPs and solitons. Interestingly, these two components are found in different spectral regions, which greatly facilitates their separation and individual study and characterization.

Chirped bright and dark solitons of (3 + 1)-dimensional coupled nonlinear Schrödinger equations in negative-index metamaterials with both electric and magnetic nonlinearity of Kerr type

NASA Astrophysics Data System (ADS)

Dai, Chao-Qing; Fan, Yan; Wang, Yue-Yue; Zheng, Jun

2018-02-01

The (3 + 1)-dimensional generalized coupled nonlinear Schrödinger equation with electric and magnetic nonlinearities of Kerr type and self-steepening effects is studied, and bright and dark soliton solutions are derived. Based on these analytical solutions, dynamical behaviors of bright and dark solitons are discussed. The amplitudes, widths and velocities of bright and dark solitons are all constants determined by the self-steepening effect parameters SE, SH. The phase chirp of a bright soliton diminishes in the pulse front of y-direction, however, it increases in the pulse back edge of y-direction. On the contrary, the phase chirp of a dark soliton increases in the pulse front of y-direction, however, it diminishes in the pulse back edge of y-direction. The phase chirps of a bright and dark soliton both shift along positive y -axis as time goes on. Moreover, the stability of the solutions is discussed.

Creation and Manipulation of Stable Dark Solitons and Vortices in Microcavity Polariton Condensates.

PubMed

Ma, Xuekai; Egorov, Oleg A; Schumacher, Stefan

2017-04-14

Solitons and vortices obtain widespread attention in different physical systems as they offer potential use in information storage, processing, and communication. In exciton-polariton condensates in semiconductor microcavities, solitons and vortices can be created optically. However, dark solitons are unstable and vortices cannot be spatially controlled. In the present work we demonstrate the existence of stable dark solitons and vortices under nonresonant incoherent excitation of a polariton condensate with a simple spatially periodic pump. In one dimension, we show that an additional coherent light pulse can be used to create or destroy a dark soliton in a controlled manner. In two dimensions we demonstrate that a coherent light beam can be used to move a vortex to a specific position on the lattice or be set into motion by simply switching the periodic pump structure from two-dimensional (lattice) to one-dimensional (stripes). Our theoretical results open up exciting possibilities for optical on-demand generation and control of dark solitons and vortices in polariton condensates.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber.

PubMed

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Wu, Xiao-Yu

2017-01-01

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of ?, but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, ? and ? are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.

Moving solitons in the discrete nonlinear Schrödinger equation.

PubMed

Oxtoby, O F; Barashenkov, I V

2007-09-01

Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When the nonlinearity is of the cubic type, this amplitude is shown to be nonzero for all velocities and therefore small-amplitude solitons moving without emitting radiation do not exist. In the case of a saturable nonlinearity, on the other hand, the radiation is found to be completely suppressed when the soliton moves at one of certain isolated "sliding velocities." We show that a discrete soliton moving at a general speed will experience radiative deceleration until it either stops and remains pinned to the lattice or--in the saturable case--locks, metastably, onto one of the sliding velocities. When the soliton's amplitude is small, however, this deceleration is extremely slow; hence, despite losing energy to radiation, the discrete soliton may spend an exponentially long time traveling with virtually unchanged amplitude and speed.

Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons

NASA Astrophysics Data System (ADS)

Veretenov, N. A.; Fedorov, S. V.; Rosanov, N. N.

2017-12-01

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., Nc knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M0 (Nc , M , and M0 are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines Nc=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M =1 , 2, and 3.

Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons.

PubMed

Veretenov, N A; Fedorov, S V; Rosanov, N N

2017-12-29

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.

Pinning of topological solitons at extrinsic defects in a quasi one-dimensional charge density wave

NASA Astrophysics Data System (ADS)

Razzaq, Samad; Wippermann, Stefan; Tae Hwan Kim Collaboration; Han Woong Yeom Collaboration

Quasi one-dimensional (1D) electronic systems are known to exhibit exotic physical phenomena, such as, e.g., Jahn Teller distortions, charge density wave (CDW) formation and non-Fermi liquid behavior. Solitonic excitations of the charge density wave ordered ground state and associated topological edge states in atomic wires are presently the focus of increasing attention. We carried out a combined ab initio and scanning tunneling microscopy (STM) study of solitonic and non-solitonic phase defects in the In/Si(111) atomic wire array. While free solitons move too fast to be imaged directly in STM, they can become trapped at extrinsic de- fects within the wire. We discuss the detailed atomistic structure of the responsible extrinsic defects and trapped solitons. Our study highlights the key role of coupled theory-experimental investigations in order to understand also the elusive fast moving solitons. S. W. gratefully acknowledges financial support from the German Research Foundation (DFG), Grant No. FOR1700.

Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials

NASA Astrophysics Data System (ADS)

Yang, Jianke; Nixon, Sean

2016-11-01

Stability of soliton families in one-dimensional nonlinear Schrödinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets (λ , - λ ,λ* , -λ*), similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non- PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.

Electromagnetic form factors of singly heavy baryons in the self-consistent SU(3) chiral quark-soliton model

NASA Astrophysics Data System (ADS)

Kim, June-Young; Kim, Hyun-Chul

2018-06-01

The self-consistent chiral quark-soliton model is a relativistic pion mean-field approach in the large Nc limit, which describes both light and heavy baryons on an equal footing. In the limit of the infinitely heavy mass of the heavy quark, a heavy baryon can be regarded as Nc-1 valence quarks bound by the pion mean fields, leaving the heavy quark as a color static source. The structure of the heavy baryon in this scheme is mainly governed by the light-quark degrees of freedom. Based on this framework, we evaluate the electromagnetic form factors of the lowest-lying heavy baryons. The rotational 1 /Nc and strange current quark mass corrections in linear order are considered. We discuss the electric charge and magnetic densities of heavy baryons in comparison with those of the nucleons. The results of the electric charge radii of the positive-charged heavy baryons show explicitly that the heavy baryon is a compact object. The electric form factors are presented. The form factor of Σc++ is compared with that from a lattice QCD. We also discuss the results of the magnetic form factors. The magnetic moments of the baryon sextet with spin 1 /2 and the magnetic radii are compared with other works and the lattice data.

Gauged baby Skyrme model with a Chern-Simons term

NASA Astrophysics Data System (ADS)

Samoilenka, A.; Shnir, Ya.

2017-02-01

The properties of the multisoliton solutions of the (2 +1 )-dimensional Maxwell-Chern-Simons-Skyrme model are investigated numerically. Coupling to the Chern-Simons term allows for existence of the electrically charge solitons which may also carry magnetic fluxes. Two particular choices of the potential term is considered: (i) the weakly bounded potential and (ii) the double vacuum potential. In the absence of gauge interaction in the former case the individual constituents of the multisoliton configuration are well separated, while in the latter case the rotational invariance of the configuration remains unbroken. It is shown that coupling of the planar multi-Skyrmions to the electric and magnetic field strongly affects the pattern of interaction between the constituents. We analyze the dependency of the structure of the solutions, the energies, angular momenta, electric and magnetic fields of the configurations on the gauge coupling constant g , and the electric potential. It is found that, generically, the coupling to the Chern-Simons term strongly affects the usual pattern of interaction between the skyrmions, in particular the electric repulsion between the solitons may break the multisoliton configuration into partons. We show that as the gauge coupling becomes strong, both the magnetic flux and the electric charge of the solutions become quantized although they are not topological numbers.

Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Al-Hashimi, M.H.; Wiese, U.-J.

2008-01-15

We consider a particle moving on a cone and bound to its tip by 1/r or harmonic oscillator potentials. When the deficit angle of the cone divided by 2{pi} is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional 'spin' and unusual degeneracies.

Relativistic many-body bound systems: electromagnetic properties. Monograph report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Danos, M.; Gillet, V.

1977-04-01

The formulae for the calculation of the electron scattering form factors, and of the static magnetic dipole and electric quadrupole moments, of relativistic many-body bound systems are derived. The framework, given in NBS Monograph 147, is relativistic quantum field theory in the Schrodinger picture; the physical particles, i.e., the solutions of the interacting fields, are given as linear combinations of the solutions of the free fields, called the parton fields. The parton--photon interaction is taken as given by minimal coupling. In addition, the contribution of the photon--vector meson vertex of the vector dominance model is derived.

Bounded-Angle Iterative Decoding of LDPC Codes

NASA Technical Reports Server (NTRS)

Dolinar, Samuel; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2009-01-01

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

PubMed

Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N

2014-09-01

We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.

Integrability and solitons for the higher-order nonlinear Schrödinger equation with space-dependent coefficients in an optical fiber

NASA Astrophysics Data System (ADS)

Su, Jing-Jing; Gao, Yi-Tian

2018-03-01

Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.

Soliton tunneling in the nonlinear Schrödinger equation with variable coefficients and an external harmonic potential.

PubMed

Zhong, Wei-Ping; Belić, Milivoj R

2010-05-01

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such solutions occurring under special conditions; specifically when the spatial solitons pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity coefficients. Our results show that the solitons display tunneling effects not only when passing through the nonlinear potential barriers or wells but also when passing through the diffractive barriers or wells. During tunneling the solitons may also undergo a controllable compression.

Breather soliton dynamics in microresonators

NASA Astrophysics Data System (ADS)

Yu, Mengjie; Jang, Jae K.; Okawachi, Yoshitomo; Griffith, Austin G.; Luke, Kevin; Miller, Steven A.; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L.

2017-02-01

The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science.

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

NASA Astrophysics Data System (ADS)

Vinayagam, P. S.; Radha, R.; Al Khawaja, U.; Ling, Liming

2018-06-01

We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called "Soliton (Breather) lattice".

Matter-wave dark solitons in boxlike traps

NASA Astrophysics Data System (ADS)

Sciacca, M.; Barenghi, C. F.; Parker, N. G.

2017-01-01

Motivated by the experimental development of quasihomogeneous Bose-Einstein condensates confined in boxlike traps, we study numerically the dynamics of dark solitons in such traps at zero temperature. We consider the cases where the side walls of the box potential rise either as a power law or a Gaussian. While the soliton propagates through the homogeneous interior of the box without dissipation, it typically dissipates energy during a reflection from a wall through the emission of sound waves, causing a slight increase in the soliton's speed. We characterize this energy loss as a function of the wall parameters. Moreover, over multiple oscillations and reflections in the boxlike trap, the energy loss and speed increase of the soliton can be significant, although the decay eventually becomes stabilized when the soliton equilibrates with the ambient sound field.

Gap solitons in PT-symmetric optical lattices with higher-order diffraction.

PubMed

Ge, Lijuan; Shen, Ming; Ma, Chunlan; Zang, Taocheng; Dai, Lu

2014-12-01

The existence and stability of gap solitons are investigated in the semi-infinite gap of a parity-time (PT)-symmetric periodic potential (optical lattice) with a higher-order diffraction. The Bloch bands and band gaps of this PT-symmetric optical lattice depend crucially on the coupling constant of the fourth-order diffraction, whereas the phase transition point of this PT optical lattice remains unchangeable. The fourth-order diffraction plays a significant role in destabilizing the propagation of dipole solitons. Specifically, when the fourth-order diffraction coupling constant increases, the stable region of the dipole solitons shrinks as new regions of instability appear. However, fundamental solitons are found to be always linearly stable with arbitrary positive value of the coupling constant. We also investigate nonlinear evolution of the PT solitons under perturbation.

Breathing Bright Solitons in a Bose Einstein Condensate

NASA Astrophysics Data System (ADS)

Chong, Gui-Shu; Hai, Wen-Hua; Xie, Qiong-Tao

2003-12-01

A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton, bisoliton and N-soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very small trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.

Bending of solitons in weak and slowly varying inhomogeneous plasma

NASA Astrophysics Data System (ADS)

Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan

2015-12-01

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Bending of solitons in weak and slowly varying inhomogeneous plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-12-15

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Soliton-dark pulse pair formation in birefringent cavity fiber lasers through cross phase coupling.

PubMed

Shao, Guodong; Song, Yufeng; Zhao, Luming; Shen, Deyuan; Tang, Dingyuan

2015-10-05

We report on the experimental observation of soliton-dark pulse pair formation in a birefringent cavity fiber laser. Temporal cavity solitons are formed in one polarization mode of the cavity. It is observed that associated with each of the cavity solitons a dark pulse is induced on the CW background of the orthogonal polarization mode. We show that the dark pulse formation is a result of the incoherent cross polarization coupling between the soliton and the CW beam and has a mechanism similar to that of the polarization domain formation observed in the fiber lasers.

Grayness-dependent emission of dispersive waves from dark solitons in optical fibers.

PubMed

Marest, T; Arabí, C Mas; Conforti, M; Mussot, A; Milián, C; Skryabin, D V; Kudlinski, A

2018-04-01

We report the experimental observation of dispersive wave emission from gray solitons propagating in the normal dispersion region of an optical fiber. Besides observing for the first time, to the best of our knowledge, the emission of a dispersive wave from an isolated dark soliton, we show that the dispersive wave frequency and amplitude strongly depend on soliton grayness. This process can be explained by the higher-order dispersion contribution into the phase-matching condition and the grayness of the soliton. Numerical simulations and theoretical predictions are in good agreement with the experiments.

Dark-soliton dynamics in Bose-Einstein condensates at finite temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jackson, B.; Proukakis, N. P.; Barenghi, C. F.

2007-05-15

The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger et al. [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified.

Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

NASA Astrophysics Data System (ADS)

Shtyrina, Olga V.; Fedoruk, Mikhail P.; Kivshar, Yuri S.; Turitsyn, Sergei K.

2018-01-01

We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.

Spectral long-range interaction of temporal incoherent solitons.

PubMed

Xu, Gang; Garnier, Josselin; Picozzi, Antonio

2014-02-01

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Exact traveling soliton solutions for the generalized Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Boudoue Hubert, Malwe; Kudryashov, Nikolai A.; Justin, Mibaile; Abbagari, Souleymanou; Betchewe, Gambo; Doka, Serge Y.

2018-03-01

In this paper, we investigate the generalized Benjamin-Bona-Mahony equation which better describes long waves with arbitrary power-law nonlinearity. As a result, we obtain exact travelling wave soliton solutions, such as anti-kink soliton solution, bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters such that they may be used to simulate many experimental situations. The main contribution, in this work, is to not apply the computer codes for construction of exact solutions and not consider the integration constants as zero, because they give all variants for solutions.

Non-autonomous matter-wave solitons in hybrid atomic-molecular Bose-Einstein condensates with tunable interactions and harmonic potential

NASA Astrophysics Data System (ADS)

Wang, Deng-Shan; Liu, Jiang; Wang, Lizhen

2018-03-01

In this paper, we investigate matter-wave solitons in hybrid atomic-molecular Bose-Einstein condensates with tunable interactions and external potentials. Three types of time-modulated harmonic potentials are considered and, for each of them, two groups of exact non-autonomous matter-wave soliton solutions of the coupled Gross-Pitaevskii equation are presented. Novel nonlinear structures of these non-autonomous matter-wave solitons are analyzed by displaying their density distributions. It is shown that the time-modulated nonlinearities and external potentials can support exact non-autonomous atomic-molecular matter-wave solitons.

Solitons of the coupled Schrödinger-Korteweg-de Vries system with arbitrary strengths of the nonlinearity and dispersion

NASA Astrophysics Data System (ADS)

Gromov, Evgeny; Malomed, Boris

2017-11-01

New two-component soliton solutions of the coupled high-frequency (HF)—low-frequency (LF) system, based on Schrödinger-Korteweg-de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode. In addition to the above-mentioned results for LF-dominated two-component solitons, which always run in one (positive) velocities, we produce HF-dominated soliton complexes, which travel in the opposite (negative) direction. They are obtained in a numerical form and by means of a quasi-adiabatic analytical approximation. The solutions with positive and negative velocities correspond, respectively, to super- and subsonic Davydov-Scott solitons.

Explicit chiral symmetry breaking in the Nambu-Jona-Lasinio model

NASA Astrophysics Data System (ADS)

Schüren, C.; Arriola, E. Ruiz; Goeke, K.

1992-09-01

We consider a chirally symmetric bosonization of the SU(2) Nambu-Jona-Lasinio model within the Pauli-Villars regularization scheme. Special attention is paid to the way in which chiral symmetry is broken explicitly. The parameters of the model are fixed in the light of chiral perturbation theory by performing a covariant derivative expansion in the presence of external fields. As a by-product we obtain the corresponding low-energy parameters and pion radii as well as some threshold parameters for pion-pion scattering. The nucleon is obtained in terms of the solitonic solutions of the action in the sector with baryon number equal to one. It is found that for a constituent quark mass M ˜ 350 MeV most of the calculated vacuum and pion properties agree reasonably well with the experimental ones and coincide with the region where localized solitons with the right size exist. For this value, however, the scalar and vector pion radii turn out to be very small. A unique determination of the sigma term is proposed, obtaining a value of σ(0) = 41.3 MeV. The scalar nucleon form factor is evaluated in the Breit frame. The extrapolation to the Cheng-Dashen point leads to σ(2 m2) - σ(0) = 7.4 MeV.

The Windy Island Soliton Experiment (WISE): Shallow Water and Basin Experiment Configuration and Preliminary Observations

DTIC Science & Technology

2009-02-19

Virginia 22203-1995 The Windy Island Soliton Experiment (WISE): Shallow Water and Basin Experiment Configuration and Preliminary Observations...case letters) The Windy Island Soliton Experiment (WISE): Shallow water and Basin Experiment Configuration and Preliminary Observations 5. FUNDING...release; distribution is unlimited 12b. DISTRIBUTION CODE 13. ABSTRACT (maximum 200 words) The Windy Islands Soliton Experiment (WISE) was

Spatial Soliton Interactions for Photonic Switching. Part I

DTIC Science & Technology

2000-03-07

solitons in geometries that allow for logically-complete, cascadable logic gates with fanout and level restoration. Detailed modeling will assist in...presented in Chapter 5. The first section covers the basic soliton interaction geometries useful for three-terminal, restoring logic, noting that the...collision and dragging geometries using orthogonally polarized solitons, which are of the general class of angular deflection gates, provide the best

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

NASA Astrophysics Data System (ADS)

Compelli, A.; Ivanov, R.; Todorov, M.

2017-12-01

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth. This article is part of the theme issue 'Nonlinear water waves'.

Relativistic stars in vector-tensor theories

NASA Astrophysics Data System (ADS)

Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji

2018-04-01

We study relativistic star solutions in second-order generalized Proca theories characterized by a U (1 )-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.

Dispersive waves induced by self-defocusing temporal solitons in a beta-barium-borate crystal.

PubMed

Zhou, Binbin; Bache, Morten

2015-09-15

We experimentally observe dispersive waves in the anomalous dispersion regime of a beta-barium-borate (BBO) crystal, induced by a self-defocusing few-cycle temporal soliton. Together the soliton and dispersive waves form an energetic octave-spanning supercontinuum. The soliton was excited in the normal dispersion regime of BBO through a negative cascaded quadratic nonlinearity. Using pump wavelengths from 1.24 to 1.4 μm, dispersive waves are found from 1.9 to 2.2 μm, agreeing well with calculated resonant phase-matching wavelengths due to degenerate four-wave mixing to the soliton. We also observe resonant radiation from nondegenerate four-wave mixing between the soliton and a probe wave, which was formed by leaking part of the pump spectrum into the anomalous dispersion regime. We confirm the experimental results through simulations.

Self-frequency shift of dark solitons in optical fibers

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Gerdjikov, Vladimir S.

1993-02-01

An analytical description of the soliton self-frequency shift (SSFS) of dark solitons is presented, using the conservation laws of the nonlinear Schrödinger equation. It is shown that the influence of intrapulse Raman scattering on dark solitons crucially depends on the sign of soliton's velocity. Our analytical expressions qualitatively explain the main features of the SSFS of the dark solitons observed recently both in experiment [A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, and R. J. Hawkins, Opt. Lett. 14, 868 (1989)] and in numerical simulation [A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, and R. J. Hawkins, Opt. Lett. 14, 868 (1989); Yu. S. Kivshar and V. V. Afanasjev, ibid. 16, 285 (1991)].

Photovoltaic spatial solitons affected by a resistor in the external circuit

NASA Astrophysics Data System (ADS)

Wang, Xiao Sheng; She, Wei Long

2002-09-01

We have found that the FWHM of one-dimensional photovoltaic spatial soliton is modified by the space-charge field in the crystal, which can be controlled by a resistor in the external circuit. In this case, the photovoltaic contribution of a background beam is taken into account. In a crystal with a positive perturbation of refractive index, the FWHM of dark soliton decreases with the resistance of the resistor, while the FWHM of bright soliton increases with the resistance. Furthermore, when R (the ratio of the effective Glass constant of a signal beam over a background beam) is higher than 1, we can switch a dark soliton to a bright soliton by decreasing the resistance or vice versa. During such process, both the wavelengths and the intensities of the signal beam and the background beam are kept unchanged.

Observation of subfemtosecond fluctuations of the pulse separation in a soliton molecule.

PubMed

Shi, Haosen; Song, Youjian; Wang, Chingyue; Zhao, Luming; Hu, Minglie

2018-04-01

In this work, we study the timing instability of a scalar twin-pulse soliton molecule generated by a passively mode-locked Er-fiber laser. Subfemtosecond precision relative timing jitter characterization between the two solitons composing the molecule is enabled by the balanced optical cross-correlation (BOC) method. Jitter spectral density reveals a short-term (on the microsecond to millisecond timescale) random fluctuation of the pulse separation even in the robust stationary soliton molecules. The root-mean-square (rms) timing jitter is on the order of femtoseconds depending on the pulse separation and the mode-locking regime. The lowest rms timing jitter is 0.83 fs, which is observed in the dispersion managed mode-locking regime. Moreover, the BOC method has proved to be capable of resolving the soliton interaction dynamics in various vibrating soliton molecules.

Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mihalache, D.; Mazilu, D.; Lederer, F.; Leblond, H.; Malomed, B. A.

2008-03-01

We present generic outcomes of collisions between stable solitons with intrinsic vorticity S=1 or S=2 in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, for the axially symmetric configuration. An essential ingredient of the complex Ginzburg-Landau equation is an effective transverse diffusivity (which is known in models of laser cavities), as vortex solitons cannot be stable without it. For the sake of comparison, results are also included for fundamental three-dimensional solitons, with S=0 . Depending on the collision momentum, χ , three generic outcomes are identified: merger of the solitons into a single one, at small χ ; quasielastic interaction, at large χ ; and creation of an extra soliton, in an intermediate region. In addition to the final outcomes, we also highlight noteworthy features of the transient dynamics.

Nonlinear Korteweg-de Vries equation for soliton propagation in relativistic electron-positron-ion plasma with thermal ions

NASA Astrophysics Data System (ADS)

Saeed, R.; Shah, Asif; Noaman-Ul-Haq, Muhammad

2010-10-01

The nonlinear propagation of ion-acoustic solitons in relativistic electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries equation has been derived by reductive perturbation technique. The effect of various plasma parameters on amplitude and structure of solitary wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that increase in the relativistic streaming factor causes the soliton amplitude to thrive and its width shrinks. The soliton amplitude and width decline as the ion to electron temperature ratio is increased. The increase in positron concentration results in reduction of soliton amplitude. The soliton amplitude enhances as the electron to positron temperature ratio is increased. Our results may have relevance in the understanding of astrophysical plasmas.

You can hide but you have to run: Direct detection with vector mediators

DOE PAGES

D’Eramo, Francesco; Kavanagh, Bradley J.; Panci, Paolo

2016-08-18

We study direct detection in simplified models of Dark Matter (DM) in which interactions with Standard Model (SM) fermions are mediated by a heavy vector boson. We consider fully general, gauge-invariant couplings between the SM, the mediator and both scalar and fermion DM. We account for the evolution of the couplings between the energy scale of the mediator mass and the nuclear energy scale. This running arises from virtual effects of SM particles and its inclusion is not optional. We compare bounds on the mediator mass from direct detection experiments with and without accounting for the running. In some casesmore » the inclusion of these effects changes the bounds by several orders of magnitude, as a consequence of operator mixing which generates new interactions at low energy. We also highlight the importance of these effects when translating LHC limits on the mediator mass into bounds on the direct detection cross section. For an axial-vector mediator, the running can alter the derived bounds on the spin-dependent DM-nucleon cross section by a factor of two or more. Lastly, we provide tools to facilitate the inclusion of these effects in future studies: general approximate expressions for the low energy couplings and a public code runDM to evolve the couplings between arbitrary energy scales.« less

You can hide but you have to run: Direct detection with vector mediators

DOE Office of Scientific and Technical Information (OSTI.GOV)

D’Eramo, Francesco; Kavanagh, Bradley J.; Panci, Paolo

We study direct detection in simplified models of Dark Matter (DM) in which interactions with Standard Model (SM) fermions are mediated by a heavy vector boson. We consider fully general, gauge-invariant couplings between the SM, the mediator and both scalar and fermion DM. We account for the evolution of the couplings between the energy scale of the mediator mass and the nuclear energy scale. This running arises from virtual effects of SM particles and its inclusion is not optional. We compare bounds on the mediator mass from direct detection experiments with and without accounting for the running. In some casesmore » the inclusion of these effects changes the bounds by several orders of magnitude, as a consequence of operator mixing which generates new interactions at low energy. We also highlight the importance of these effects when translating LHC limits on the mediator mass into bounds on the direct detection cross section. For an axial-vector mediator, the running can alter the derived bounds on the spin-dependent DM-nucleon cross section by a factor of two or more. Lastly, we provide tools to facilitate the inclusion of these effects in future studies: general approximate expressions for the low energy couplings and a public code runDM to evolve the couplings between arbitrary energy scales.« less

Aberrated surface soliton formation in a nonlinear 1D and 2D photonic crystal

PubMed Central

Lysak, Tatiana M.; Trykin, Evgenii M.

2018-01-01

We discuss a novel type of surface soliton—aberrated surface soliton—appearance in a nonlinear one dimensional photonic crystal and a possibility of this surface soliton formation in two dimensional photonic crystal. An aberrated surface soliton possesses a nonlinear distribution of the wavefront. We show that, in one dimensional photonic crystal, the surface soliton is formed at the photonic crystal boundary with the ambient medium. Essentially, that it occupies several layers at the photonic crystal boundary and penetrates into the ambient medium at a distance also equal to several layers, so that one can infer about light energy localization at the lateral surface of the photonic crystal. In the one dimensional case, the surface soliton is formed from an earlier formed soliton that falls along the photonic crystal layers at an angle which differs slightly from the normal to the photonic crystal face. In the two dimensional case, the soliton can appear if an incident Gaussian beam falls on the photonic crystal face. The influence of laser radiation parameters, optical properties of photonic crystal layers and ambient medium on the one dimensional surface soliton formation is investigated. We also discuss the influence of two dimensional photonic crystal configuration on light energy localization near the photonic crystal surface. It is important that aberrated surface solitons can be created at relatively low laser pulse intensity and for close values of alternating layers dielectric permittivity which allows their experimental observation. PMID:29558497

Higgs constraints from vector boson fusion and scattering

DOE PAGES

Campbell, John M.; Ellis, R. Keith

2015-04-07

We present results on 4-lepton + 2-jet production, the partonic processes most commonly described as vector boson pair production in the Vector Boson Fusion (VBF) mode. That final state contains diagrams that are mediated by Higgs boson exchange. We focus particularly on the high-mass behaviour of the Higgs boson mediated diagrams, which unlike on-shell production, gives information about the Higgs couplings without assumptions on the Higgs boson total width. We assess the sensitivity of the high-mass region to Higgs coupling strengths, considering all vector boson pair channels, W - W +, W ± W ±, W ± Z and ZZ.more » Because of the small background, the most promising mode is W + W + which has sensitivity to Higgs couplings because of Higgs boson exchange in the t-channel. Furthermore, using the Caola-Melnikov (CM) method, the off-shell couplings can be interpreted as bounds on the Higgs boson total width. We estimate the bound that can be obtained with current data, as well as the bounds that could be obtained at √s=13 TeV in the VBF channel for data samples of 100 and 300 fb -1. The CM method has already been successfully applied in the gluon fusion (GGF) production channel. The VBF production channel gives important complementary information, because both production and decay of the Higgs boson occur already at tree graph level.« less

Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, Wei; Shen, Ming; Kong, Qian; Shi, Jielong; Wang, Qi; Krolikowski, Wieslaw

2014-04-01

We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Qi; Shi, Jielong; Shen, Ming

2017-11-01

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

Pseudo-phase-matched four-wave mixing in soliton wavelength-division multiplexing transmission.

PubMed

Mamyshev, P V; Mollenauer, L F

1996-03-15

In a soliton transmission system using lumped amplifiers, pseudo phase matching allows four-wave mixing fields from soliton-soliton collisions to grow uncontrollably and inf lict severe penalties. Through numerical simulation, we show that this growth can be eliminated, or at least greatly reduced, through the use of fiber whose dispersion is tapered, either continuously or in steps, in conformity with the fiber loss curve.

Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

NASA Astrophysics Data System (ADS)

Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj

2016-05-01

We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice.

PubMed

Gulevich, D R; Yudin, D; Skryabin, D V; Iorsh, I V; Shelykh, I A

2017-05-11

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator - material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes - topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.

Scattering of lattice solitons and decay of heat-current correlation in the Fermi-Pasta-Ulam-α -β model

NASA Astrophysics Data System (ADS)

Jin, Tao; Yu, Jian; Zhang, Nan; Zhao, Hong

2017-08-01

As is well known, solitons can be excited in nonlinear lattice systems; however, whether, and if so, how, this kind of nonlinear excitation can affect the energy transport behavior is not yet fully understood. Here we study both the scattering dynamics of solitons and heat transport properties in the Fermi-Pasta-Ulam-α -β model with an asymmetric interparticle interaction. By varying the asymmetry degree of the interaction (characterized by α ), we find that (i) for each α there exists a momentum threshold for exciting solitons from which one may infer an α -dependent feature of probability of presentation of solitons at a finite-temperature equilibrium state and (ii) the scattering rate of solitons is sensitively dependent on α . Based on these findings, we conjecture that the scattering between solitons will cause the nonmonotonic α -dependent feature of heat conduction. Fortunately, such a conjecture is indeed verified by our detailed examination of the time decay behavior of the heat current correlation function, but it is only valid for an early time stage. Thus, this result may suggest that solitons can have only a relatively short survival time when exposed in a thermal environment, eventually affecting the heat transport in a short time.

On a family of KP multi-line solitons associated to rational degenerations of real hyperelliptic curves and to the finite non-periodic Toda hierarchy

NASA Astrophysics Data System (ADS)

Abenda, Simonetta

2017-09-01

We continue the program started in Abenda and Grinevich (2015) of associating rational degenerations of M-curves to points in GrTNN(k , n) using KP theory for real finite gap solutions. More precisely, we focus on the inverse problem of characterizing the soliton data which produce Krichever divisors compatible with the KP reality condition when Γ is a certain rational degeneration of a hyperelliptic M-curve. Such choice is motivated by the fact that Γ is related to the curves associated to points in GrTP(1 , n) and in GrTP(n - 1 , n) in Abenda and Grinevich (2015). We prove that the reality condition on the Krichever divisor on Γ singles out a special family of KP multi-line solitons (T-hyperelliptic solitons) in GrTP(k , n) , k ∈ [ n - 1 ] , naturally connected to the finite non-periodic Toda hierarchy. We discuss the relations between the algebraic-geometric description of KP T-hyperelliptic solitons and of the open Toda system. Finally, we also explain the effect of the space-time transformation which conjugates soliton data in GrTP(k , n) to soliton data in GrTP(n - k , n) on the Krichever divisor for such KP solitons.

Versatile soliton emission from a WS2 mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Guo, Bo; Li, Shi; Fan, Ya-xian; Wang, Pengfei

2018-01-01

Recently, few-layer tungsten disulfide (WS2), as a shining 2D material, has been discovered to possess both the saturable absorption ability and large nonlinear refractive index. Here, we demonstrate versatile soliton pulses in a passively mode-locked fiber laser with a WS2-deposited microfiber. The few-layer WS2 is prepared by the liquid-phase exfoliation method and transferred onto a microfiber by the optical deposition method. Study found, the WS2-deposited microfiber can operate simultaneously as a mode-locker and a high-nonlinear device. In experiment, by further inserting the WS2 device into the fiber laser, besides the dual-wavelength soliton, noise-like soliton pulse, conventional soliton and its harmonic form are obtained by properly adjusting the pump strength and the polarization states. For the dual-wavelength soliton pulses and noise-like pulse, the maximum output power of 14.2 mW and pulse energy of 4.74 nJ is obtained, respectively. In addition, we also achieve the maximum harmonic number (135) of conventional soliton, corresponding to a repetition rate of ∼ 497 . 5 MHz. Our study shows clearly that WS2-deposited microfiber can be as a high-nonlinear photonic device for studying a plenty of nonlinear soliton phenomena.

The propagation and backscattering of soliton-like pulses in a chain of quartz beads and related problems. (I). Propagation

NASA Astrophysics Data System (ADS)

Manciu, Marian; Sen, Surajit; Hurd, Alan J.

1999-12-01

We confirm that for vanishingly small loading and large impact condition, it may be possible to generate solitons in a chain of grains that are characterized by Hertzian contacts. For uniform or progressive loading conditions throughout the chain, one generates soft-solitons which are weakly dispersive in space and time. Under conditions of weak impact, one generates acoustic pulses through the chain. We describe the displacements, velocities and accelerations suffered by the individual grains when subjected to solitons, soft-solitons and acoustic pulses and describe the effects of restitution on the propagating pulse.

Detection of fractional solitons in quantum spin Hall systems

NASA Astrophysics Data System (ADS)

Fleckenstein, C.; Traverso Ziani, N.; Trauzettel, B.

2018-03-01

We propose two experimental setups that allow for the implementation and the detection of fractional solitons of the Goldstone-Wilczek type. The first setup is based on two magnetic barriers at the edge of a quantum spin Hall system for generating the fractional soliton. If then a quantum point contact is created with the other edge, the linear conductance shows evidence of the fractional soliton. The second setup consists of a single magnetic barrier covering both edges and implementing a long quantum point contact. In this case, the fractional soliton can unambiguously be detected as a dip in the conductance without the need to control the magnetization of the barrier.

Soliton solution for the spin current in a ferromagnetic nanowire.

PubMed

Li, Zai-Dong; Li, Qiu-Yan; Li, Lu; Liu, W M

2007-08-01

We investigate the interaction of a periodic solution and a one-soliton solution for the spin-polarized current in a uniaxial ferromagnetic nanowire. The amplitude and wave number of the periodic solution for the spin current give different contributions to the width, velocity, and amplitude of the soliton. Moreover, we found that the soliton can be trapped only in space with proper conditions. Finally, we analyze the modulation instability and discuss dark solitary wave propagation for a spin current on the background of a periodic solution. In some special cases, the solution can be expressed as the linear combination of the periodic and soliton solutions.

Gauged Q-balls

NASA Technical Reports Server (NTRS)

Lee, Kimyeong; Stein-Schabes, Jaime A.; Watkins, Richard; Widrow, Lawrence M.

1988-01-01

Classical non-topological soliton configurations are considered within the theory of a complex scalar field with a gauged U symmetry. Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically. The soliton configuration is such that inside the soliton the local U symmetry is broken, the gauge field becomes massive and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface. Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q-matter in bulk form. Also briefly discussed are solitons with fermions in a U gauge theory.

Dark solitons in the presence of higher-order effects.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2013-12-01

Dark soliton propagation is studied in the presence of higher-order effects, including third-order dispersion, self-steepening, linear/nonlinear gain/loss, and Raman scattering. It is found that for certain values of the parameters a stable evolution can exist for both the soliton and the relative continuous-wave background. Using a newly developed perturbation theory we show that the perturbing effects give rise to a shelf that accompanies the soliton in its propagation. Although, the stable solitons are not affected by the shelf it remains an integral part of the dynamics otherwise not considered so far in studies of higher-order nonlinear Schrödinger models.

Indirect assessment of bulk strain soliton velocity in opaque solids

NASA Astrophysics Data System (ADS)

Belashov, A. V.; Beltukov, Y. M.; Petrov, N. V.; Samsonov, A. M.; Semenova, I. V.

2018-03-01

This paper presents a methodology allowing for determination of strain soliton velocity in opaque solid materials. The methodology is based on the analysis of soliton evolution in a layer of a transparent material adhesively bonded to the layer of a material under study. It is shown that the resulting soliton velocity in the complex waveguide equals to the arithmetic mean of soliton velocities in the two component materials. The suggested methodology is best suited for analysis of materials with relatively close elastic parameters and can be applied in research of nonlinear wave processes in opaque composites on the basis of transparent matrices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szankowski, Piotr; Trippenbach, Marek; Infeld, Eryk

We introduce a class of solitonlike entities in spinor three-component Bose-Einstein condensates. These entities generalize well-known solitons. For special values of coupling constants, the system considered is completely integrable and supports N soliton solutions. The one-soliton solutions can be generalized to systems with different values of coupling constants. However, they no longer interact elastically. When two so-generalized solitons collide, a spin component oscillation is observed in both emerging entities. We propose to call these newfound entities oscillatons. They propagate without dispersion and retain their character after collisions. We derive an exact mathematical model for oscillatons and show that the well-knownmore » one-soliton solutions are a particular case.« less

Numerical simulation of dark envelope soliton in plasma

NASA Astrophysics Data System (ADS)

Wang, Fang-Ping; Han, Juan-fang; Zhang, Jie; Gao, Dong-Ning; Li, Zhong-Zheng; Duan, Wen-Shan; Zhang, Heng

2018-03-01

One-dimensional (1-D) particle-in-cell simulation is used to study the propagation of dark envelop solitons described by the nonlinear Schrödinger equation (NLSE) in electron-ion plasmas. The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the dark envelope soliton in plasma. It is demonstrated by our numerical simulation that there is dark envelope soliton in electron-ion plasmas. The numerical results are in good agreements with the analytical ones from the NLSE which is obtained from the reductive perturbation method. The limitation of the amplitude of dark envelop solitons in plasma is noticed.

Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the "phoenix soliton".

PubMed

Peleg, Or; Segev, Mordechai; Bartal, Guy; Christodoulides, Demetrios N; Moiseyev, Nimrod

2009-04-24

We formulate wave propagation in arrays of subwavelength waveguides with sharp index contrasts and demonstrate the collapse of bands into evanescent modes and lattice solitons with superluminal phase velocity. We find a self-reviving soliton ("phoenix soliton") comprised of coupled forward- and backward-propagating light, originating solely from evanescent bands. In the linear regime, all Bloch waves comprising this beam decay, whereas a proper nonlinearity assembles them into a propagating self-trapped beam. Finally, we simulate the dynamics of such a beam and observe breakup into temporal pulses, indicating a new kind of slow-light gap solitons, trapped in time and in one transverse dimension.

Intermittent burst of a super rogue wave in the breathing multi-soliton regime of an anomalous fiber ring cavity.

PubMed

Lee, Seungjong; Park, Kyoungyoon; Kim, Hyuntai; Vazquez-Zuniga, Luis Alonso; Kim, Jinseob; Jeong, Yoonchan

2018-04-30

We report the intermittent burst of a super rogue wave in the multi-soliton (MS) regime of an anomalous-dispersion fiber ring cavity. We exploit the spatio-temporal measurement technique to log and capture the shot-to-shot wave dynamics of various pulse events in the cavity, and obtain the corresponding intensity probability density function, which eventually unveils the inherent nature of the extreme events encompassed therein. In the breathing MS regime, a specific MS regime with heavy soliton population, the natural probability of pulse interaction among solitons and dispersive waves exponentially increases owing to the extraordinarily high soliton population density. Combination of the probabilistically started soliton interactions and subsequently accompanying dispersive waves in their vicinity triggers an avalanche of extreme events with even higher intensities, culminating to a burst of a super rogue wave nearly ten times stronger than the average solitons observed in the cavity. Without any cavity modification or control, the process naturally and intermittently recurs within a time scale in the order of ten seconds.

Highly coherent mid-IR supercontinuum by self-defocusing solitons in lithium niobate waveguides with all-normal dispersion.

PubMed

Guo, Hairun; Zhou, Binbin; Zeng, Xianglong; Bache, Morten

2014-05-19

We numerically investigate self-defocusing solitons in a lithium niobate (LN) waveguide designed to have a large refractive index (RI) change. The waveguide evokes strong waveguide dispersion and all-normal dispersion is found in the entire guiding band spanning the near-IR and the beginning of the mid-IR. Meanwhile, a self-defocusing nonlinearity is invoked by the cascaded (phase-mismatched) second-harmonic generation under a quasi-phase-matching pitch. Combining this with the all-normal dispersion, mid-IR solitons can form and the waveguide presents the first all-nonlinear and solitonic device where no linear dispersion (i.e. non-solitonic) regimes exist within the guiding band. Soliton compressions at 2 μm and 3 μm are investigated, with nano-joule single cycle pulse formations and highly coherent octave-spanning supercontinuum generations. With an alternative design on the waveguide dispersion, the soliton spectral tunneling effect is also investigated, with which few-cycle pico-joule pulses at 2 μm are formed by a near-IR pump.

Two solitons oblique collision in anisotropic non-extensive dusty plasma

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Taibany, W. F.; Behery, E. E.; Fouda, S. M.

2017-03-01

Using an extended Poincaré-Lighthill-Kue method, the oblique collision of two dust acoustic solitons (DASs) in a magnetized non-extensive plasma with the effect of dust pressure anisotropy is studied. The dust fluid is supposed to have an arbitrary charge. A couple of Korteweg-de Vries (KdV) equations are derived for the colliding DASs. The phase shift of each soliton is obtained. It is found that the dust pressure anisotropy, the non-extensive parameter for electrons and ions, plays an important role in determining the collision phase shifts. The present results show that, for the negative dust case, the phase shift of the first soliton decreases, while that of the second soliton increases as either the dust pressure ratio increases or the ion non-extensive parameter decreases. On the other hand, for the positive dust case, the phase shift of the first soliton decreases, while the phase shift of the second soliton increases as either the dust pressure ratio or the ion non-extensive parameter increases. The application of the present findings to some dusty plasma phenomena occurring in space and laboratory plasmas is briefly discussed.

Dark-Bright Soliton Dynamics Beyond the Mean-Field Approximation

NASA Astrophysics Data System (ADS)

Katsimiga, Garyfallia; Koutentakis, Georgios; Mistakidis, Simeon; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team

2017-04-01

The dynamics of dark bright solitons beyond the mean-field approximation is investigated. We first examine the case of a single dark-bright soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the decay of each of the initial mean-field dark-bright solitons into fast and slow fragmented dark-bright structures. A variety of excitations including dark-bright solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.

A unified view of acoustic-electrostatic solitons in complex plasmas

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2003-03-01

A fluid dynamic approach is used in a unified fully nonlinear treatment of the properties of the dust-acoustic, ion-acoustic and Langmuir-acoustic solitons. The analysis, which is carried out in the wave frame of the soliton, is based on total momentum conservation and Bernoulli-like energy equations for each of the particle species in each wave type, and yields the structure equation for the `heavy' species flow speed in each case. The heavy (cold or supersonic) species is always compressed in the soliton, requiring concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave. The treatment clearly elucidates the crucial role played by the heavy species sonic point in limiting the collective species Mach number, which determines the upper limit for the existence of the soliton and its amplitude, and also shows the essentially similar nature of each soliton type. An exact solution, which highlights these characteristic properties, shows that the three acoustic solitons are in fact the same mathematical entity in different physical disguises.

Spatial solitons in a semiconductor microresonator

NASA Astrophysics Data System (ADS)

Taranenko, V. B.; Ganne, I.; Kuszelewicz, R.; Weiss, C. O.

We show experimentally the existence of bright and dark spatial solitons in a passive quantum-well-semi-conductor resonator of large Fresnel number with mixed absorptive defocusing nonlinearity. Several of the solitons can exist simultaneously as required for applications.

Photorefractive steady state solitons up to telecommunication wavelengths in planar SBN waveguides

NASA Astrophysics Data System (ADS)

Wesner, M.; Herden, C.; Kip, D.; Krätzig, E.; Moretti, P.

2001-02-01

We experimentally demonstrate strong photorefractive self-focusing and soliton formation in Rh-doped strontium-barium niobate waveguides at telecommunication wavelengths up to λ=1.5 μm. A comparison of soliton formation at different wavelengths in the visible and infrared region is carried out. We measure the electrooptic coefficient r33, analyze the soliton width, the accessible intensity range, and the wavelength dependence of the so-called `dark intensity'.

Long-range sound-mediated dark-soliton interactions in trapped atomic condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allen, A. J.; Jackson, D. P.; Barenghi, C. F.

2011-01-15

A long-range soliton interaction is discussed whereby two or more dark solitons interact in an inhomogeneous atomic condensate, modifying their respective dynamics via the exchange of sound waves without ever coming into direct contact. An idealized double-well geometry is shown to yield perfect energy transfer and complete periodic identity reversal of the two solitons. Two experimentally relevant geometries are analyzed which should enable the observation of this long-range interaction.

Core filling and snaking instability of dark solitons in spin-imbalanced superfluid Fermi gases

NASA Astrophysics Data System (ADS)

Reichl, Matthew D.; Mueller, Erich J.

2017-05-01

We use the time-dependent Bogoliubov-de Gennes equations to study dark solitons in three-dimensional spin-imbalanced superfluid Fermi gases. We explore how the shape and dynamics of dark solitons are altered by the presence of excess unpaired spins which fill their low-density core. The unpaired particles broaden the solitons and suppress the transverse snake instability. We discuss ways of observing these phenomena in cold-atom experiments.

Soliton-induced relativistic-scattering and amplification.

PubMed

Rubino, E; Lotti, A; Belgiorno, F; Cacciatori, S L; Couairon, A; Leonhardt, U; Faccio, D

2012-01-01

Solitons are of fundamental importance in photonics due to applications in optical data transmission and also as a tool for investigating novel phenomena ranging from light generation at new frequencies and wave-trapping to rogue waves. Solitons are also moving scatterers: they generate refractive index perturbations moving at the speed of light. Here we found that such perturbations scatter light in an unusual way: they amplify light by the mixing of positive and negative frequencies, as we describe using a first Born approximation and numerical simulations. The simplest scenario in which these effects may be observed is within the initial stages of optical soliton propagation: a steep shock front develops that may efficiently scatter a second, weaker probe pulse into relatively intense positive and negative frequency modes with amplification at the expense of the soliton. Our results show a novel all-optical amplification scheme that relies on soliton induced scattering.

Dynamical behavior of the random field on the pulsating and snaking solitons in cubic-quintic complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Bakhtiar, Nurizatul Syarfinas Ahmad; Abdullah, Farah Aini; Hasan, Yahya Abu

2017-08-01

In this paper, we consider the dynamical behaviour of the random field on the pulsating and snaking solitons in a dissipative systems described by the one-dimensional cubic-quintic complex Ginzburg-Landau equation (cqCGLE). The dynamical behaviour of the random filed was simulated by adding a random field to the initial pulse. Then, we solve it numerically by fixing the initial amplitude profile for the pulsating and snaking solitons without losing any generality. In order to create the random field, we choose 0 ≤ ɛ ≤ 1.0. As a result, multiple soliton trains are formed when the random field is applied to a pulse like initial profile for the parameters of the pulsating and snaking solitons. The results also show the effects of varying the random field of the transient energy peaks in pulsating and snaking solitons.

Optical analogue of relativistic Dirac solitons in binary waveguide arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tran, Truong X., E-mail: truong.tran@mpl.mpg.de; Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen; Longhi, Stefano

2014-01-15

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An opticalmore » analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.« less

Scattering of matter waves in spatially inhomogeneous environments

DOE PAGES

Tsitoura, F.; Krüger, P.; Kevrekidis, P. G.; ...

2015-03-30

In this article, we study scattering of quasi-one-dimensional matter waves at an interface of two spatial domains, one with repulsive and one with attractive interatomic interactions. It is shown that the incidence of a Gaussian wave packet from the repulsive to the attractive region gives rise to generation of a soliton train. More specifically, the number of emergent solitons can be controlled, e.g., by the variation of the amplitude or the width of the incoming wave packet. Furthermore, we study the reflectivity of a soliton incident from the attractive region to the repulsive one. We find the reflection coefficient numericallymore » and employ analytical methods, which treat the soliton as a particle (for moderate and large amplitudes) or a quasilinear wave packet (for small amplitudes), to determine the critical soliton momentum (as a function of the soliton amplitude) for which total reflection is observed.« less