联立薛定谔系统新精确解及其所描述的孤子脉冲和时间孤子

利用拓展的Riccati映射法，讨论了联立薛定谔系统，得到了其新的精确解，并根据所得到的解模拟出孤子脉冲、飞秒孤子和时间孤子，以及时间孤子间的弹性相互作用. 关键词： 联立薛定谔方程 拓展Riccati映射 孤子脉冲 时间孤子     

(2+1)维Boiti-Leon-Pempinelli系统的混沌行为及孤子间的相互作用

利用改进的变系数的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统(BLP)的新显式精确解.根据得到的解，研究了BLP系统的混沌行为及孤子间的相互作用. 关键词： 改进的映射法 Boiti-Leon-Pempinelli系统 混沌行为 相互作用     

变系数(2+1)维Broer-Kaup系统的特殊孤子结构及孤子的裂变和湮没现象

利用改进的Riccati方程映射法，得到了变系数(2+1)维 Broer-Kaup 系统的孤波解、周期波解和变量分离解.根据得到的孤波解，构造出了系统的几种不同形状的孤子结构，研究了孤子的裂变和湮没现象. 关键词： 变系数(2+1)维 Broer-Kaup 系统 孤子结构 裂变 湮没     

(3+1)维Burgers系统的新精确解及其特殊孤子结构

将改进的Riccati方程映射法和变量分离法推广到(3+1)维Burgers系统，得到了该系统的新显式精确解.根据得到的孤波解，构造出Burgers系统的几种特殊孤子结构，例如柱状孤子、状孤子和内嵌孤子等，研究了孤子间的相互作用.     

扩展的(2+1)维浅水波方程的尖峰孤子解及其相互作用

利用改进的 Riccati方程映射法和变量分离法, 得到了扩展的(2+1)维浅水波方程的变量分离解(包括孤波解, 周期波解和有理函数解). 根据得到的孤波解, 构造出了方程的几种不同形状的尖峰孤子结构, 研究了孤子的相互作用.     

(3+1)维Burgers系统的新精确解及其特殊孤子结构

将改进的Riccati方程映射法和变量分离法推广到(3+1)维Burgers系统,得到了该系统的新显式精确解.根据得到的孤波解,构造出Burgers系统的几种特殊孤子结构,例如柱状孤子、状孤子和内嵌孤子等,研究了孤子间的相互作用. 关键词： 改进的映射法 (3+1)维Burgers系统 孤子结构 相互作用     

(2+1)维 Zakharov-Kuznetsov 方程的精确解和孤子结构

在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解. 根据得到的解,研究了ZK方程的特殊孤子结构. 关键词： 改进的Riccati方程映射法 Zakharov-Kuznetsov方程 精确解 孤子结构     

(2+1)维Boiti-Leon-Pempinelle系统的钟状和峰状圈孤子

借助于Painlev Bcklund变换和多线性变量分离方法, 求得了(2+1)维非线性Boiti Leon Pempinelle系统的一般变量分离解．根据得到的一般解, 可以构建出丰富的局域相干结构, 如峰状孤子、紧致子等. 得到了两种新的局域结构——钟状圈孤子和峰状圈孤子, 并简要讨论了这两种圈孤子的一些特殊演化性质． 关键词： Boiti Leon Pempinelle系统 多线性变量分离法 钟状圈孤子 峰状圈孤子     

(2+1)维孤子系统的多孤子解和分形结构

利用投射方程法和变量分离法,得到了(2+1)维非对称Nizhnik-Novikov-Veselov系统的新显式精确解.根据得到的孤波解,构造出了该系统的多孤子和分形孤子.     

(3+1)维Burgers系统的瞬内嵌孤子和瞬锥形孤子

利用投射方程法和变量分离法,得到了(3+1)维Burgers系统的变量分离解(包括孤波解、周期波解和有理函数解).根据孤波解和有理函数解,构造出Burgers系统新颖的局域结构,例如瞬内嵌孤子和瞬锥形孤子.     

Matter wave solitons in coupled system with external potentials

We present Lax-pair corresponding to the coupled Gross-Pitaevskii equation (CGPE) which governs the evolution of the macroscopic wave function of two components Bose-Einstein condensates trapped in time-dependent harmonic potential. Kinds of soliton solutions can be derived from the Lax-pair through Darboux transformation conveniently. Furthermore, soliton management in two-component Bose-Einstein condensate would be realized base on that the shape and motion of soliton in both components are investigated analytically. Moreover, it is found that there is a transformation existed between the nonautonomous coupled system and Manakov model.     

Small-amplitude solitons in nonlinear-saturation glass fibers

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Nonautonomous deformed solitons in a Bose-Einstein condensate

We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton＇s center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.     

Domain wall solitons in quantum electron plasmas

We show the existence of new stationary solutions in the form of domain wall soliton in the nonlinear Schrödinger-Poisson equations describing the dynamics of quantum electron plasmas. It is found that the domain wall soliton exists at strong coupling constant regime and shows a different dynamical behavior in comparison with the previously found dark and gray solitons. The robustness and the conservation of the energy of the domain wall solitons is demonstrated by numerical simulations.     

Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose--Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature ({\em Phys. Rev. Lett.} {\bf 94} (2005) 050402 and {\em Chin. Phys. Lett.} {\bf 22} (2005) 1855).     

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.     

Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance

We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetric soliton by changing the parameterφ.In addition,the collision between soliton molecules(or asymmetric soliton)and several soliton solutions is observed.Finally,some related pictures are presented.     

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.     

Gap solitons in parity time complex superlattice with dual periods

A theory is presented to investigate the existence and propagation stability of gap solitons in a parity-time （PT） com- plex superlattice with dual periods. In this superlattice, the real and imaginary parts are both in the form of superlattices with dual periods. In the self-focusing nonlinearity, PT solitons can exist in the semi-infinite gap. However, only those gap solitons with low powers can propagate stably, whereas the high-power solitons present periodic oscillation and simultane- ously suffer energy decay. In the self-defocusing nonlinearity, PT solitons only exist in the first gap and all these solitons are stable.     

Nonautonomous solitons in the continuous wave background of the variable-coefficient higher-order nonlinear Schro¨dinger equation

We reduce the variable-coefficient higher-order nonlinear Schrdinger equation (VCHNLSE) into the constantcoefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.