Exact travelling wave solutions for （1＋ 1）-dimensional dispersive long wave equation

A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.     

Conditional Similarity Solutions of （2＋1）—Dimensional General nonintegrable KdV Equation

The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model.To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters.In this paper,we make a modification for the usual direct method to find some conditional similarity solutions of a (2 1)-dimensional general nonintegrable KdV equation.     

Periodic Wave Solutions for （2＋1）-Dimensional Boussinesq Equation and （3＋ 1）-Dimensional Kadomtsev-Petviashvili Equation

For describing various complex nonlinear phenomena in the realistic world, the higher-dimensional nonlinear evolution equations appear more attractive in many fields of physical and engineering sciences. In this paper, by virtue of the Hirota bilinear method and Riemann theta functions, the periodic wave solutions for the （2＋1）-dimensional Boussinesq equation and （3＋1）-dimensional Kadomtsev Petviashvili （KP） equation are obtained. Furthermore, it is shown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.     

The exact solutions to （2＋1）-dimensional nonlinear Schroedinger equation

By using the extended F-expansion method,the exact solutions,including periodic wave solutions expressed by Jaeobi elliptic functions,for (2 1)-dimensional nonlinear Schroedinger equation are derived.In the limit cases,the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.     

New Exact Periodic Solitary-Wave Solutions for New （2＋1）-Dimensional KdV Equation

The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.     

Explicit Solutions for Generalized （2＋1）-Dimensional Nonlinear Zakharov-Kuznetsov Equation

The exact solutions of the generalized （2＋1）-dimensional nonlinear Zakharov-Kuznetsov （Z-K） equation are explored by the method of the improved generalized auxiliary differential equation. Many explicit analytic solutions of the Z-K equation are obtained. The methods used to solve the Z-K equation can be employed in further work to establish new solutions for other nonlinear partial differential equations.     

（2+1）维NLBQ方程和KP方程的多dromion结构和相互作用的研究

从（2+1）维双线性形式的非局域Bussinesq(NLBQ)方程和KP方程的隐线孤子解出发,可以找到与某种势所相应的各方向都指数衰减的dromion解.利用图形分析的方法,对这些dromion之间的相互作用进行了详细的研究.发现这两种模型中的dromion间的相互作用只引起位相漂移,不引起形状和速度的变化,也不引起旋转.即dromion间的相互作用是弹性的,没有能量、动量和角动量的交换. 关键词：     

(3+1)维Nizhnik-Novikov-Veselov方程的孤子解和周期解

采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解. 关键词： (3+1)维Nizhnik-Novikov-Veselov方程 非线性Klein-Gordon方程 孤子解 周期解     

A Series of Exact Solutions for a New （2＋1）-Dimensional Calogero KdV Equation

An algebraic method is proposed to solve a new （2＋1）-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions.     

(3+1)维Jimbo-Miwa方程的精确解及局域激发

在符号计算软件 Maple 的帮助下,利用投射方程法和变量分离法,得到了(3+1)维 Jimbo-Miwa(JM)方程的新显式精确解. 根据得到的孤立波解,研究了 JM 方程新颖的局域激发. 关键词： 投射方程法 Jimbo-Miwa方程 精确解 局域激发     

New Solitary Solutions of （2＋1）-Dimensional Variable Coefficient Nonlinear Schrodinger Equation with an External Potential

By a series of transformations, the （2＋1）-dimensional variable coefficient nonlinear Schr？dinger equation can turn to the Klein-Gordon equation. Many new double travelling wave solutions of the Klein-Gordon equation are obtained. Thus, the new solitary solutions of the variable coefficient nonlinear Schr？inger equation with an external potential can be found.     

(3+1)维 KdV 方程新的精确解和孤子解

用普通Korteweg-de Vries(KdV)方程作变换,构造(3 1)维KdV方程的解,获得了新的孤子解、Jaoobi椭圆函数解、三角函数解和Weierstrass椭圆函数解.     

Fission and Fusion of Solitons for the （1＋1）—Dimensional Kupershmidt Equation

By means of the heat conduction equation and the standard truncated Painleve expansion,the (1 1)-dimensional Kupershmidt equation is solved.Some significant exact multi-soliton solutions are given.Especially,for the interaction of the multi-solitons of the Kupershmidt equation,we find that a single(resonant)kink or bell soliton may be fissioned to several kink or bell solitons,Inversely,several kink or bell solitons may also be fused to one kink or bell soliton.     

A Series of Soliton-like and Double-like Periodic Solutions of a （2＋1）-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2 1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions‘soliton-like solutions, double-like periodic and trigonometric-like function solutions.     

（2＋1）维sine—Gordon方程的三种函数混合解

基于一构造的Wronskian形式展开法，获得了（2＋1）维sine—Gordon方程的一系列新形式的混合解．这些解是三角函数、双曲函数及Jacobi椭圆函数等三种函数的组合形式．     

New Exact Solutions to （2＋1）-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.     

Two classes of fractal structures for the （2＋1）-dimensional dispersive long wave equation

Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.     

A method for constructing exact solutions and application to Benjamin Ono equation

By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.     

Rational and Periodic Solutions for a （2＋1）-Dimensional Breaking Soliton Equation Associated with ZS-AKNS Hierarchy

The double Wronskian solutions whose entries satisfy matrix equation for a （2＋1）-dimensional breaking soliton equation （（2＋ 1）DBSE） associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for （2＋1）DBSE are obtained by taking special eases in general double Wronskian solutions.