变系数GKP方程的精确解

doi:10.6040/j.issn.1671-9352.0.2017.565

摘要/Abstract

摘要： 对一类变系数GKP方程求解,首先构造出解的形式并结合不同的辅助方程的新解及相应的Bäcklund变换,在数学计算软件的帮助下获得了该方程的无穷序列类孤子新精确解。这些解的类型包括Jacobi椭圆函数型、三角函数型、指数函数型、双曲函数型等。然后又使用假设孤立波方法研究这一类变系数GKP方程,进而得到了另类的孤立波解。

关键词: 变系数GKP方程, 辅助方程, Bä, cklund变换, 无穷序列精确解

Abstract: In order to solve a kind of GKP equation with variable coefficients, the form of the solution is first constructed then combined with the new solutions of different auxiliary equations and corresponding Bäcklund transformations. With the help of mathematical calculation software, the new exact solutions of infinite sequence soliton-like of the equation are obtained. The types of these solutions include Jacobi elliptic function type, trigonometric function type, exponential function type, hyperbolic function type, etc. Using the hypothetical solitary wave method, this kind of GKP equation with variable coefficients is studied. Then alternative solitary wave solutions are obtained.

Key words: GKP equation with variable coefficients, auxiliary equation, Bä, cklund transformation, infinite sequence exact solutions

中图分类号:

O175.2

杨飞,刘希强. 变系数GKP方程的精确解[J]. 《山东大学学报(理学版)》, 2019, 54(2): 111-120.

YANG Fei, LIU Xi-qiang. Exact solution of GKP equation with variable coefficients[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 111-120.

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