Lax可积系统的有限变换对称群及严格解

本文用一种简单直接的方法研究了非线性物理系统Davey-Stewartson方程及（２＋１）维的Camassa-Holm方程，并给出了它们的有限变换对称群及对称。     

Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation

The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations. In this paper, we use a new form of variable separation to study novel soliton molecules and their interactions in (2+1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation. Dromion molecules, ring molecules, lump molecules, multi-instantaneous molecules, and their interactions are obtained. Then we draw corresponding images with maple software to study their dynamic behavior.     

求非线性系统对称群的新方法

(1)从Lax可积系统的Lax对出发, 寻找非线性系统的对称及精确解, 利用这种方法可以解决不少(2＋1)维的可积系统, 它的优点在于比较简洁方便, 这从KP方程的求解对比就可以看出. (2)从CK直接法入手, 将这种方法进行修正, 利用这种修正的CK直接法求非线性系统的对称和精确解; 这种方法的最大优点在于不但可以用于可积系统, 而且也适用于不可积系统, 还可以求出离散群. 另外, 这种方法也适用于高维的不可积模型.     

任意方程法及BKP方程新的精确解

In this paper,auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation.We study the(2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions.The method used here can be also extended to other nonlinear partial differential equations.     

Symmetry Transformation and New Exact Multiple Kink and Singular Kink Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy

In this paper, we consider a system of (2+1)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Jaulent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation.     

New Periodic Solution to Jacobi Elliptic Functions of a （2d-1）-Dimensional BKP Equation and a Generalized Klein-Gordon Equation

With the help of the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to obtain the Jacobi doubly periodic wave solutions of the （2＋1）-dimensional B-type Kadomtsev-Petviashvili （BKP） equation and the generalized Klein-Gordon equation. The method is also valid for other （1＋1）-dimensional and higher dimensional systems.     

A Simple Method to Generate Lie Point Symmetry Groups of the （3＋1）-Dimensional Jimbo-Miwa Equation

Taking the (3 1)-dimensional Jimbo-Miwa equation as a simple example, we develop a modified direct method to find symmetry groups and symmetry algebras. Some exact solutions of the model are given by the simple method.     

带自由参数高阶变系数耦合非线性Schr(o)dinger方程的Painlevé可积性

借助于奇异分析的手段判断带自由参数高阶变系数耦合非线性Schrdinger方程的Painleve可积性.得到了在一定参数约束下,仅有两个子系统是Painleve可积的.     

带自由参数高阶变系数耦合非线性Schr(o)dinger方程的Painlevé可积性

借助于奇异分析的手段判断带自由参数高阶变系数耦合非线性Schr(o)dinger方程的Painlevé可积性.得到了在一定参数约束下,仅有两个子系统是Painlevé可积的.     

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.