理论数学

Vol.1 No.2 (July 2011)

一类变系数组合KdV方程新的精确解析解
New Exact Analytic Solutions to a Coupled KdV Equation with Variable Coefficients

 

作者:

洪宝剑

 

关键词:

变系数组合KdV方程精确解析解Riccati方程变速孤立波Coupled KdV Equations with Variable Coefficients Exact Analytic Solutions Riccati Equa-tions Solitary Wave Solutions with Variable Speed

 

摘要:

在齐次平衡法和分离变量的基础上,通过两个推广的Riccati方程,借助Mathematica软件,求出了一类变系数组合KdV方程的一些精确解析解,包括各种类孤立子解、类周期解和变速孤立波解,部分解为首次发现。

Based on the homogeneous balance principle and general variable separation approach, with the aid of two generalized Riccati equations and Mathematica software, we first find some exact analytic solutions to a coupled KdV equation with variable coefficients, including several kinds of soliton-like solutions, periodical-like solutions and solitary wave solutions with variable speed. Some of them are found for the first time.

文章引用:

洪宝剑 (2011) 一类变系数组合KdV方程新的精确解析解。 理论数学, 1, 163-166. doi: 10.12677/pm.2011.12032

 

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