Multisoliton Solutions of the (2+1)-Dimensional KdV Equation

Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2+1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations.

LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS

By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogeneous balance method for the higher order (2 + 1)-dimensional Broer-Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quite rich localized coherent structures were revealed. This method, which can be generalized to other (2 + I) -dimensional nonlinear evolution equation, is simple and powerful.

Bifurcation of travelling wave solutions for (2+1)-dimension nonlinear dispersive long wave equation

In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for （2＋1）-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurcation parameter sets are shown,and under various parameter conditions,all exact explicit formulas of solitary travelling wave solutions and kink travelling wave solutions and periodic travelling wave solutions are listed.

New Exact Solutions for the Generalized （2 ＋ 1）-dimensional Nonlinear Schroedinger Equation with Variable Coefficients

With the help of the variable-coefficient generalized projected Ricatti equation expansion method, we present exact solutions for the generalized （2＋1）-dimensional nonlinear SchrSdinger equation with variable coefficients. These solutions include solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time.

Exotic Localized Coherent Structures of the （2＋1）—Dimensional Dispersive Long—Wave Equation

This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.

(2+1)维Gardner(2DG)方程行波解的定性分析

应用平面动力系统方法研究(2+1)维Gardner(2DG)方程的精确行波解.通过讨论在不同参数区域中的相图获得了各种光滑解存在的充分条件,并在给定的参数条件下获得了其孤立波解和周期波解的参数表达式.

达布变换与(2+1)维Gardner方程的新解(英文)

近期,耿献国和曹策问将(2+1)维Gardner方程分解到两个(1+1)维孤子方程.本文计算出这两个(1+1)维孤子方程的Lax对,并利用Lax对的规范变换构造了该(1+1)维孤子方程的新达布变换.应用达布变换和分解获得了(2+1)维Gardner方程的一些新显式解,其中包括多孤子解.