Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate

We study two types of bright solitons in an attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear Schr odinger equations with the variational method and the imaginary time evolution method,fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength.The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate.     

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.     

Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We investigate the moving matter-wave solitons in spin-orbit coupled Bose-Einstein condensates(BECs) by a perturbation method.Starting with the one-dimensional Gross-Pitaevskii equations,we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spinorbit coupling.The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs.We find different types of moving solitons:dark-bright,bright-bright and dark-dark solitons.Interestingly,moving dark-dark soliton for attractive intra- and inter-species interactions is found,which depends on the Raman coupling.The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin-orbit coupling.     

Slowly moving matter--wave gap soliton propagation in weak random nonlinear potential

We systematically investigate the motion of slowly moving matter--wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross--Pitaevskii equation.     

Observation of soliton fusion in a Josephson array

The behavior of topological solitons in a parallel array of a Josephson junction is studied experimentally. We observe the fusion of two relativistic solitons of the same polarity into a single soliton. The soliton carries two quanta of magnetic flux and, most strikingly, travels 18% faster than an ordinary soliton under the same driving force. We also find a variety of bunched states composed of solitons of the same polarity, moving with fixed separation.     

Packing, unpacking, and steering of multicolor solitons in optical lattices

We discuss potential applications of multicolor solitons supported by periodic lattices imprinted in quadratic nonlinear media. Such lattice solitons can be packed together with appropriate relative phases to form stable soliton trains that can be treated as bit sequences. We describe controllable splitting of the trains into their soliton constituents and the angle- and power-controlled steering and trapping of solitons moving across the lattice into the desired guiding channel.     

Oscillation properties of matter-wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.     

PARTICULAR SOLITONS IN NONLINEAR LATTICE

One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define V_n at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e^-(r_n)-1 and their initial amplitude of e^-(r_n)-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.     

A (1+1)-dimensional integrable system with fifth order spectral problems and four dispersion relations

A new (1+1)-dimensional integrable model is investigated, of which the Lax integrability is shown by the existence of its fifth order spectral problems. Its bilinear form is obtained via introducing an auxiliary variable. The multiple soliton solutions are obtained by solving its bilinear system. It is shown that there are four different dispersion relations for multiple solitons. The amplitudes of the solitons are only wave number dependent while the velocities of the solitons are not only wave number dependent but also dispersion relation dependent. Because of the existence of four dispersion relations, the interactions among solitons are much more abundant because for any fixed wave number there are four different velocities including two left moving and two right moving. Especially, the existence of the multiple velocities makes the velocity resonant conditions can be readily satisfied to form many types of bound states including soliton molecules, soliton-breather molecules and breather molecules.     

超常介质中暗孤子的形成和传输特性研究

利用一种扩展的双曲函数级数方法求解超常介质中的传输方程，得到了各种不同情形下的暗孤子解，分析了可控自陡效应和二阶非线性色散效应对孤子形成和传输特性的影响.结果表明，超常介质中负的自陡效应使得暗孤子的中心位置随传输距离向脉冲前沿方向漂移，与常规介质中自陡效应(恒为正)的作用相反；特别是，由于二阶非线性色散的作用，使得在没有线性群速度色散的情形下同样可形成孤子，而且在反常线性色散情形也可形成暗孤子.     

Head-on collision of ring dark solitons in Bose--Einstein condensates

The ring dark solitons and their head-on collisions in a Bose--Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincar\'e--Lighthill--Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate $r$ according to the $r^{-1/3}$ law and depend on the initial soliton amplitude and radius.     

Interactions of solitons with complex defects in Bragg gratings

We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them, is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of the incident soliton can be captured when its velocity attains half the light speed in the fiber (the case most relevant to the experiment), and the captured soliton quickly relaxes to a stationary state. A subsequent collision between another free soliton and the pinned one is examined too, demonstrating that the impinging soliton always bounces back, while the pinned one either remains in the same state, or is kicked out forward, depending on the collision velocity and phase shift between the solitons.     

Hemispherical ion acoustic solitons

Hemispherical solitons are studied experimentally using a double-plasma device provided with a hemispherical dividing screen. Their properties are compared with those of spherical solitons and differ appreciably. Auxiliary pulses appear behind the soliton, each propagating faster than the soliton but eventually approaching the soliton speed     

Slowly moving matter-wave gap soliton propagation in weak random optical lattices

We systematically investigate slowly moving matter-wave gap soliton propagation in weak random optical lattices. With the weak randomness, an effective-particle theory is constructed to show that the motion of a gap soliton is similar to a particle moving in random potentials. Based on the effective-particle theory, the effects of the randomness on gap solitons are obtained and the trajectories of gap solitons are well predicted. Moreover, the general laws that describe the movement depending on the weak randomness are obtained. We find that with an increase of the random strength, the ensemble-average velocity reduces slowly and the reflection probability becomes larger. The theoretical results based on the effective-particle theory are confirmed by the numerical simulations based on the Gross-Pitaevskii equation.     

Dynamic soliton-like modes

Incoherent optical spatial solitons require noninstantaneous nonlinearity, i.e., the local intensity fluctuation of the solitons must be faster than the medium can respond. Observing partially incoherent bicomponent solitons, we find that there exists a threshold speed. When the fluctuation of the soliton intensity, resulting from the time-varying interference of its constituent modes, is below the threshold, the soliton beam and its induced waveguide oscillate violently. Just above the threshold, the soliton-induced waveguide is observed to be dragged by the soliton beam.     

有限宽度布拉格原子层中光子囚禁与移动孤子的研究

研究二能级原子层宽度对一维共振吸收布拉格反射镜中自感应透明光孤子形成的影响.结果表明：在有限宽度的二能级原子层中仍可激发稳定的移动孤子，其激发条件对原子层宽度依赖不大；然而静止孤子的存在条件却敏感地依赖于原子层的宽度，二能级原子层宽度只有小于某一特定值时，光脉冲才能演化成静止孤子. 关键词： 有限宽度 周期结构 移动孤子 静止孤子     

Creating very slow optical gap solitons with a grating-assisted coupler

We show that optical gap solitons can be produced with velocities down to 4% of the group velocity of light using a grating-assisted coupler, i.e., a fiber Bragg grating that is linearly coupled to a non-Bragg fiber over a finite domain. Forward- and backward-moving light pulses in the non-Bragg fiber(s) that reach the coupling region simultaneously couple into the Bragg fiber and form a moving soliton, which then propagates beyond the coupling region. Two of these solitons can collide to create an even slower or stopped soliton.     

二阶孤子的传输和相互作用

用分步傅里叶变换法求解二阶孤子传输的非线性薛定谔方程, 得到了在此条件下孤子传输的数值图形, 发现二阶孤子在传输中被压缩, 幅值振荡变化。2个二阶孤子在传输过程中没有出现象2个一阶孤子那样周期性碰撞, 但2个二阶孤子时间间隔较小时, 随传输距离在2个二阶孤子中间周期性地衍生出第3个孤子。研究证明：二阶孤子的传输具有与一阶孤子明显不同的特征。