Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin–orbit coupled Bose–Einstein condensate

We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling. With the modulation of the spin–orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin–orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin–orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.     

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.     

Two-component coupled photovoltaic soliton pair in two-photon photorefractive materials under open circuit conditions

The existence and nonlinear dynamics of two-component incoherently coupled composite solitons in two-photon photorefractive materials under open circuit conditions have been investigated. In the steady-state regime, these incoherently coupled solitons can propagate in bright–dark, bright–bright and dark–dark configurations. These photovoltaic soliton families can be established provided that the carrier beams share the same polarization and wavelength. The influence of the gating beam on the dynamics of stable solitons is discussed. Numerical simulations show that these solitons are stable for small perturbation on amplitude.     

Self-generation of fundamental dark solitons in magnetic films

The self-generation of single, fundamental, stable, spin-wave-envelope black and gray dark solitons has been realized for the first time. These solitons were generated from microwave magnetostatic surface waves (MSSWs) propagated in an in-plane magnetized yttrium iron garnet film MSSW delay line in a resonant ring. These fundamental dark solitons were made possible by a new and general filtering technique for a high gain nonlinear resonant ring. The amplitude and phase profiles together with the power spectra of the self-generated microwave pulses confirm their fundamental dark soliton nature.     

Dark optical solitons with power law nonlinearity using G′/G-expansion

This paper studies the dynamics of dark optical solitons. The G′/G-expansion approach is utilized. The byproduct of this approach is the singular periodic solution of the governing nonlinear Schrödinger's equation for its corresponding parameter regime. The constraint conditions are also in place for the existence of dark solitons.     

暗孤子在高斯变迹光纤光栅中的演化

运用快速傅里叶方法数值模拟了暗孤子在高斯变迹光纤光栅中的演化以及暗孤子之间的相互作用。结果表明,在一定条件下光纤光栅的正常色散区可以维持暗孤子的稳定传输,并且孤子的稳定性与f的取值(孤子离禁带的位置)和非线性系数有关。输入两个暗孤子时,孤子之间的相互作用随f的增大而加强,当f继续增大时孤子中心和背景处出现震荡现象并演化产生灰孤子;f越大,两个孤子的稳定性对非线性效应越敏感。     

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.     

Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential

This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential.The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates.The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential.The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates.The collision of two dark solitons is nearly elastic.     

Double Humped Grey and Black Solitons in Kerr Nonlinear Media

The existence of a new class of double humped grey and dark solitons in a Kerr nonlinear medium has been predicted in this paper. Following well known variational procedure, the dynamics of the propagating soliton has been converted to a Hamiltonian formulation. A set of ordinary differential equations is then derived, which was subsequently examined to predict the existence of double humped grey and dark solitons. Linear stability analysis, numerical appreciation and phase plane dynamics show that these solitons are stable.     

非局域非线性介质中空间暗孤子的理论和实验研究

对非局域非线性介质中的空间暗孤子进行了研究.理论上运用牛顿迭代法求解非局域非线性薛定谔方程,得到了不同传播常数下的非局域空间暗孤子的数值解,发现在任何非局域程度以及任何传播常数条件下,都存在暗孤子的解,而且孤子的束宽与非局域程度存在一定的关系.实验上,在染料溶液中观测到了空间暗孤子在非局域非线性介质中的形成.利用输入功率所引起的非线性效应强度的变化,分析了背景光波形对暗孤子的影响,数值模拟结果与实验结果相符合. 关键词： 非局域非线性 空间暗孤子     

A novel temporal dark-bright solitons conversion system via an add/drop filter for signal security use

We propose a new design of a security scheme by using the nonlinear behaviors of temporal dark and bright solitons within a micro-ring resonator system for signal security application. When a dark soliton pulse is input into the proposed system, the chaotic signal is generated, where the required bright soliton pulse can be retrieved and detected by the add/drop filtering device. The chaotic wave form can be cancelled by using an add/drop device, which can be connected and used in the communication link. By using the appropriate ring parameters, simulation results obtained have shown that the soliton conversion can be performed. The ring radii used are within the ranges from 5 to 10 μms and A_eff=0.10-0.50 μm². In application, the chaotic signal is generated and formed by the dark soliton within a nonlinear micro-ring device. This can be seen by using the add/drop device, where the bright soliton is formed and detected, which is available to use in communication link. The different temporal soliton response time is seen, the response times of 169 and 84 ns are noted for temporal dark and bright solitons, respectively, which can also be used to form the security key.     

Complete and orthonormal eigenfunctions of excitations to a one-dimensional dark soliton

We study linear excitations to a one-dimensional dark soliton described by a defocusing nonlinear Schödinger equation. By solving an eigenvalue problem for the excitations we obtain all eigenvalues and eigenfunctions and prove rigorously that these eigenfunctions are orthonormal and form a complete set. We then use the eigenfunctions to obtain the exact form of linear excitations for any given initial condition and to investigate the transverse stability of the dark soliton. The rigorous results reported in the present work can be applied to study the dynamics of dark solitons in various nonlinear optical media and Bose-Einstein condensates.     

Diffraction effects on soliton propagation

An averaged-Lagrangian method is used to analyze diffraction effects on propagation of solitons of various types in homogeneous media. It is shown that diffraction can counteract the self-focusing of dark and gray envelope solitons described by the nonlinear Schrödinger equation and solitons described by the Korteweg-de Vries equation when the soliton intensities do not exceed certain values. Conversely, diffraction enhances the self-focusing of dark and gray envelope solitons described by the modified Korteweg-de Vries equation, kinks described by the sine-Gordon equation, and domain walls in the u 4 model, which is explained by mutual correlation between transverse and longitudinal soliton dynamics. Critical parameters that determine soliton stability with respect to self-focusing are found for several models.     

光纤中自变陡效应支持的小振幅孤波

基于连续波背景上的小振幅近似，研究了自变陡效应对正常色散区和非常色散区孤波传输动力学的决定作用。在计及损耗和增益，以及Ｒａｍａｎ自泵的光纤中，两种色散区中均存在明孤波和暗孤波，尤其是发现了与通常明、暗类型相反的小振幅明、暗孤波。 关键词：     

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.     

Condition for convective instability of dark solitons

Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal group velocity of the disturbance waves propagating along a dark soliton. The growth rate of the length of dark solitons generated by the flow of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is confirmed by the results of numerical simulations.     

电磁感应透明介质中的弱光空间暗孤子环

利用多重尺度方法,解析地研究了Λ型三能级冷原子气及一束较强耦合光组成的电磁感应透明介质体系中的非线性动力学性质.结果表明：一束较弱的探测光能在电磁感应透明介质中形成弱光空间暗孤子,当弱光空间暗孤子沿轴向传播时,它会逐渐演化成一个稳定的弱光空间暗孤子环,这是衍射效应和自散焦效应相互平衡的结果. 关键词： 电磁感应透明 弱光空间暗孤子环 多重尺度方法     

The dynamics of ring dark soliton in inhomogeneous Bose-Einstein condensates

The dynamics of the ring dark soliton in an inhomogeneous Bose-Einstein condensates (BEC) with thin disk-shaped potential trapping is investigated analytically and numerically. Analytical result shows that the ring dark soliton is governed by a variable coefficients Korteweg-de Vries (KdV) equation. The effect of the ring curvature (nonplanar geometry) and the inhomogeneous of the background on soliton amplitude and the emitted radiation profiles are obtained analytically. The theoretical results are confirmed by the direct numerical results.     

Dark optical solitons in power law media with time-dependent coefficients

This Letter talks about the dynamics of dark optical solitons that are governed by the nonlinear Schrödinger's equation with power law nonlinearity. The solitons are considered in presence of linear attenuation, third order dispersion and self-steepening terms, all with time-dependent coefficients. The solitary wave ansatz is used to carry out the integration and an exact soliton solution is obtained. It is only necessary that these time-dependent coefficients are Riemann integrable.