多波长系统孤子耦合方程的可积性

多波长系统孤子耦合方程存在Lax对，具有可积性，利用Hirota双线性方法求出了孤子耦合方程的单孤子解和双孤子解. 关键词： Lax对 Hirota双线性变换 可积性     

高阶(2+1)维Broer-Kaup方程的孤波解

利用一个简单的变换将高阶(2+1)维Broer-Kaup方程变为一个简单的方程，并且结合齐次平 衡法给出了高阶(2+1)维Broer-Kaup方程的一些新的孤子解.这一方法可应用于其他非线性物 理模型. 关键词： Broer-Kaup方程 (2+1)维 孤子解 齐次平衡法     

周期分布放大系统的精确解及其相互作用

考虑带有变增益侦耗和频率啁啾的非线性薛定谔方程，利用达布变换求得该方程的N-孤子解，并给出带有变增益钡耗和频率啁啾的一孤子解和二孤子解的精确表达式。特别地，详细讨论了孤子周期分布放大系统的动力学行为。结果表明，带有变增益／损耗和频率啁啾的孤子解可以应用于周期分布放大系统，同时保留了孤子的特性。     

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     

（2+1）维耗散长波方程与(2+1)维Broer-Kaup方程新的类多孤子解

进一步拓广齐次平衡法的应用，并对关键的操作步骤进行了改进，从而简便地求出了（2+1 ）维耗散长波方程和（2+1）维Broer-Kaup方程新的类多孤子解-这种解更具有一般性，它包 含着已有文献给出的类多孤子解- 关键词： 齐次平衡法 类多孤子解 （2+1）维耗散长波方程 （2+1）维Broer-Kaup方程     

高阶效应影响下飞秒孤子间的相互作用

本文从高阶非线性薛定谔方程（HNLS）出发，给出了其Lax对，同时运用Darborx变换求得了N-孤子解和双孤子解的显式表达式，并且给出了在一定初始条件下谱参数的近拟本片值。最后通过数值模拟对解析结果作了验证，结果表明：高阶效应的联合作用在一定程度上能够减弱飞秒孤子间的相互作用。     

变系数（2＋1）维Broe-Kaup方程的新精确解

通过一个简单的变换，变系数(2 1)维Broer-Kaup方程被简化为人们熟知的变系数Burgers方程。利用近年来广泛使用的齐次平衡法和tanh-函数法，获得了变系数(2 1)维Broer-Kaup方程的一些新的精确解。     

四阶非线性薛定谔方程中呼吸子解的特性研究

基于同时包含四阶色散项和四阶非线性项的非线性薛定谔层级结构的四阶可积方程(LPD方程),首先利用达布变换法得到LPD方程的单呼吸子解,并对呼吸子的动力学特性进行研究,得到呼吸子与W型孤子、抖动的W型孤子和周期波的转换关系;其次,借助达布变换的递推关系得到LPD方程的双呼吸子解,并利用呼吸子与孤子之间的转换关系,研究呼吸子与孤子以及呼吸子与周期波的碰撞特性;最后,对双呼吸子的碰撞特性进行更为详细的研究,得到双呼吸子的交叉碰撞、平行叠加及双呼吸子的简并态等动力学特性。     

(2+1)维Broer-Kaup方程的广义dromion解结构

利用推广的齐次平衡方法,首先将(2+1)维Broer-Kaup方程线性化,然后构造出丰富的广义孤子解,包括单孤子解,单曲线孤子解,单dromion解,多dromion解。此方法直接而简单,可推广应用一大类(2+1)维非线性可积方程。     

Boiti-Leon-Pempinelli系统的新变量分离解及其方形孤子和分形孤子

利用拓展的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统新的变量分离 解．根据得到的分离变量解，构造出该系统新型的孤子结构——方孤子和分形孤子． 关键词： Boiti-Leon-Pempinelli系统 拓展Riccati映射 方形孤子 分形孤子     

New Multi-soliton Solutions for the （2＋1）-Dimensional Kadomtsev-Petviashvili Equation

In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili （KP） equation are obtained.     

A Unified Explicit Construction of 2N-Soliton Solutions for Evolution Equations Determined by 2×2 AKNS System

An explicit N-fold Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed. By using the Darboux transformation, the solutions of the evolution equations are reduced to solving alinear algebraic system, from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given. Furthermore, a reduction technique for MKdV equation is presented, and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique. A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed.     

Solving Kadomtsev—Petviashvili Equation via a New Decomposition and Darboux Transformation

Recently,a new decomposition of the (2 1)-dimensional Kadomtsev-Petviashvili(KP) equation to a (1 1)-dimensional Broer-Kaup (BK) equation and a (1 1)-dimensional high-order BK equation was presented by Lou and Hu.In our paper,a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems.As application,new explicit soliton-like solutions with five arbitrary parameters for the BK equation,high-order BK equation and KP equation are obtained.     

Darboux Transformation and Multi-Solitons for Complex mKdV Equation

An explicR N-fold Darboux transformation with multi-parameters for coupled mKdV equation is constructed with the help of a gauge transformation of the Ablowitz-Kaup-Newell-Segur （AKNS） system spectral problem. By using the Darboux transformation and the reduction technique, some multi-soliton solutions for the complex mKdV equation are obtained.     

Darboux Transformation and New Soliton-like Solutions for (1+1)-Dimensional Higher-Order Broer-Kaup System

In this letter, we construct a kind of new Darboux transformation for the (1+1)-dimensional higher-order Broer-Kaup (HBK) system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the (1+1)-dimensional HBK system are obtained.     

Darboux transformation for two‐level system

We develop the Darboux procedure for the case of the two‐level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two‐level system, transforming only one real potential into another real potential. We apply the obtained Darboux transformation to known exact solutions of the two‐level system. Thus, we find three classes of new solutions for the two‐level system and the corresponding new potentials that allow such solutions.     

A Unified and Explicit Construction of N-Soliton Solutions for the Nonlinear Schrfdinger Equation

An explicit N-fold Darboux transformation with multiparameters for nonlinear Schrodinger equation is constructed with the help of its Lax pairs and a reduction technique. According to this Darboux transformation, the solutions of the nonlinear Schrfdinger equation are reduced to solving a linear algebraic system, from which a unified and explicit formulation of N-soliton solutions with multiparameters for the nonlinear Schrfdinger equation is given.``     

A Unified and Explicit Construction of N-Soliton Solutions for the Nonlinear Schrödinger Equation

An explicit N-fold Darboux transformation with multiparameters for nonlinear Schrödinger equation is constructed with the help of its Lax pairs and a reduction technique. According to this Darboux transformation, the solutions of the nonlinear Schrödinger equation are reduced to solving a linear algebraic system, from which a unified and explicit formulation of N-soliton solutions with multiparameters for the nonlinear Schrödinger equation is given.     

Darboux Transformation and Explicit Solutions for Drinfel＇d-Sokolov-Wilson Equation

A generalized Drinfel＇d Sokolov-Wilson （DSW） equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DEW equation such as rational solutions, soliton solutions, periodic solutions.     

BINARY DARBOUX TRANSFORMATION AND QUASIDETERMINANT SOLUTIONS OF THE CHIRAL FIELD

The standard binary Darboux transformation is composed and is used to obtain exact multisoliton solutions of the chiral field model in two dimensions. The solutions are expressed in terms of quasideterminants. It has been shown that the standard binary Darboux transformation is equivalent to the elementary binary Darboux transformation.