变系数Kadomtsev–Petviashvili(KP)方程的精确解_数学专业.doc

摘要

本文应用辅助方程方法研究了一个变系数Kadomtsev–Petviashvili(KP)方程,获得了六组指数函数类的精确解,在不同的参数条件下,每一组解都能化为一些孤波解和周期波解.

关键词:辅助方程法;指数函数法;齐次平衡原则;精确解;Riccati方程;变系数Kadomtsev–Petviashvili(KP)方程

ABSTRACT

In this paper, a variable coefficient Kadomtsev–Petviashvili（KP）equation is investigated. Auxiliary equation method are used to determine six families of exact solutions of exp-function type for this equation. Under different parametric conditions, every family of solution can be reduced to some solitary wave solutions and periodic wave solutions.

Keywords: Auxiliary equation method;Exp-function method;Homogeneous balance principle;Exact solution;Riccati equation;Variable coefficient Kadomtsev Petviash-vili(KP)equation