Zakharov-Kuznetsov方程新的周期解和孤立波解  

A New Periodic and Solitary Wave Solutions to Zakharov-Kuznetsov Equation

作　　者：高云[1] 乐励华[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《东华理工大学学报（自然科学版）》2010年第4期393-397,共5页Journal of East China University of Technology(Natural Science)

摘　　要：随着非线性科学的发展,许多物理、工程技术和数学模型都可以转化为非线性方程,如非线性常微分方程、偏微分方程等。非线性方程的求解已经成为非线性科学领域的一个重要研究课题。Zakharov-Kuznetsov方程(简称ZK方程)作为非线性方程中重要的一类,是由Zakharov和Kuznetsov在1974年提出的,该方程是KdV方程在二维空间的典型推广形式之一,因此研究该方程具有广泛的理论意义和实践意义。本文用拓展的双曲函数正切法,借助Riccati方程的解,结合Mathematical数学软件,得到Zakharov-Kuznetsov方程新的显示精确解,包括周期解和孤立波解.所给的方法还可以用来求解其它的一大类非线性发展方程。With development of nonlinear science,a lot of physics,engineering,and mathematics models can be changed into nonlinear equations,such as nonlinear ODE,PDE.Solving nonlinear equations has become an important research topic in the field of nonlinear science.In 1974 Zakharov and Kuznetsov posed the nonlinear Zakharov-Kuznetsov equation（ZK equations in short）,which is an important nonlinear equations for a class.This equation is one of the best known two-dimensional generalizations of the KdV equation.Studying this equation is important not only in theory but also in practice.In this paper,by using extend hyperbolic tangent function,with the aid of solutions of Riccati equation and Mathematica software,Zakharov-Kuznetsov equation obtains the new explicit exact solutions,which contain periodic solutions and solitary wave solutions.The method can be used to solve other nonlinear developing equation.

关 键 词：ZAKHAROV-KUZNETSOV方程 RICCATI方程 周期解 孤立波解 

分 类 号：O175[理学—数学]