摘  要:本文以一个Riccati方程作为辅助方程并利用它的一些精确解,求出了(3+1) 维K(m,n)方程大量的精确解,包括一些孤波解和周期解,此种方法也能应用到其它非线性偏微分方程中.

关键词:(3+1)维K(m,n)方程; Riccati方程; 辅助方程方法; 精确解; 齐次平衡原则

Abstract:In this paper, the large numbers of exact solutions of the (3+1) dimentional K(m, n) equation are obtained by a Riccati equation as auxiliary equation and its some exact solutions, including some solitary wave solutions and periodic solutions. This method can also be applied to other nonlinear evolution equations.

Keywords: (3+1) dimentional K(m, n) equation; Riccati equation; Auxiliary equation 

method; Exact solution; Homogeneous balance principle

目录

第一章 引言-1

    1.1 研究方程的现实意义-1

    1.2 研究现状-1

    1.3 研究内容-2

第二章 方法介绍-3

第三章 (3+1)维的精确解-6

第四章 结论-16

参看文献-17

致谢-19