推广的F -展开法及变系数KdV和mKdV的精确解

数学物理学报

推广的F -展开法及变系数KdV和mKdV的精确解

张金良;王明亮 ;王跃明

河南科技大学理学院洛阳 471003

收稿日期:2004-09-27 修回日期:2005-10-10
通讯作者: 张金良
基金资助:
河南省教育厅自然科学基金(2006110002)和河南科技大学重大专项预研基金(2004ZD002)资助

The Extended F-expansion Method and the Exact Solutions to the

KdV and mKdV Equation with Variable Coefficients

Zhang Jinliang ; Wang Mingliang ; Wang Yueming

Department of Mathematics and Physics, Henan University of Science and Technology, Luoyang 471003

Received:2004-09-27 Revised:2005-10-10
Contact: Zhang Jinliang

摘要/Abstract

摘要： 该文首先推广了新近提出的F -展开法,利用该方法导出了变系数KdV和mKdV方程的类椭圆函数解;并在极限的情况下,得到变系数KdV和 mKdV方程变波速和变波长的类孤子解以及其他形式解.

关键词: F -展开法, 类椭圆函数解, 类孤子解, 变系数KdV方程, 变系数mKdV方程

Abstract: In this paper, the F-expansion method proposed recently is improved and applied to derive the cnoidal-like solutions of the general KdV and mKdV equations with variable coefficients. In the limit case, the soliton-like solutions with variable propagating speed and amplitude are obtained.

Key words: F-expansion method, Cnoidal-like solution, Soliton-like solution, KdV equation with variable coefficients, mKdV equation with variable coefficients

中图分类号:

35Q20

张金良;王明亮 ;王跃明. 推广的F -展开法及变系数KdV和mKdV的精确解[J]. 数学物理学报, 2006, 26(3): 353-360.

Zhang Jinliang ; Wang Mingliang ; Wang Yueming.

The Extended F-expansion Method and the Exact Solutions to the

KdV and mKdV Equation with Variable Coefficients

[J]. Acta mathematica scientia,Series A, 2006, 26(3): 353-360.