广义Ginzburg-Landau方程和Rangwala Rao方程的显式精确解

数学物理学报 ›› 2003, Vol. 23 ›› Issue (6): 679-691.

广义Ginzburg-Landau方程和Rangwala Rao方程的显式精确解

张卫国

上海理工大学理学院上海 200093

出版日期:2003-12-25 发布日期:2003-12-25
基金资助:
上海市高等学校科学技术发展基金资助项目

Explicit Exact Solutions for Generalized Ginzburg Landau Equation and Rangwala Rao Equation

ZHANG Wei-Guo

上海理工大学理学院上海 200093

Online:2003-12-25 Published:2003-12-25
Supported by:
上海市高等学校科学技术发展基金资助项目

摘要/Abstract

摘要：

该文通过适当代换并结合假设待定法，求出了具高阶非线性项的Liénard方程a″(ξ)+la(ξ)+ma\+\{2p+1\}(ξ)+na\+\{4p+1\}(ξ)=0的三类精确解. 据此求出了广义GinzburgLandau方程、RangwalaRao方程及若干导数schr〖AKo¨D〗dinger型方程的孤波解和三角函数型周期波解.

关键词: 精确解;Liénard方程; , 广义Ginzburg Landau方程, Rangwala Rao方程

Abstract:

In this paper, the authors first obtain three kinds of explicit exact solution for the liénard equation a″(ξ)+la(ξ)+ma^{2p+1}(ξ)+na^{4p+1}(ξ)=0
by proper transformation and undetermined assumption method. By means of these solutions, the authors obtain solitary wave solutions and perio dic wave solutions of triangle function type for generalized GinzburgLandau eq u ation and RangwalaRao equation and several nonlinear derivation Schr[AKo¨D]di nger type equations.

Key words: Exact solution, Liénard equation, Generalized Ginzburg Landau equation, Rangwala Rao equation

中图分类号:

35Q20

张卫国. 广义Ginzburg-Landau方程和Rangwala Rao方程的显式精确解[J]. 数学物理学报, 2003, 23(6): 679-691.

ZHANG Wei-Guo. Explicit Exact Solutions for Generalized Ginzburg Landau Equation and Rangwala Rao Equation[J]. Acta mathematica scientia,Series A, 2003, 23(6): 679-691.

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