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

DOI: 10.12677/pm.2011.12032, PDF, 下载: 2,591  浏览: 10,437  科研立项经费支持

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。
Abstract: 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. 一类变系数组合KdV方程新的精确解析解[J]. 理论数学, 2011, 1(2): 163-166. http://dx.doi.org/10.12677/pm.2011.12032

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