用双曲函数法求KdV- mKdV方程的钟状孤波解和激波状孤波解

华南理工大学学报(自然科学版) ›› 2004, Vol. 32 ›› Issue (7): 78-80.

用双曲函数法求KdV- mKdV方程的钟状孤波解和激波状孤波解

朱燕娟

广东工业大学应用物理学院广东广州510090

收稿日期:2004-03-12 出版日期:2004-07-20 发布日期:2015-09-09
通信作者: 朱燕娟（1958－）女硕士副教授主要从事纳米材料制备与应用及非线性物理研究． E-mail:tczyj＠jnu.edu.cn
作者简介:朱燕娟（1958－）女硕士副教授主要从事纳米材料制备与应用及非线性物理研究．
基金资助:
广东省自然科学基金资助项目（20010026）

Two Kinds of Solitary Wave Solutions to the KdV-mKdV Equation Obtained by Hyperbolic Function Method

Zhu Yan-juan

Faculty of Applied PhysicsGuangdong Univ．of Tech．Guangzhou510090GuangdongChina

Received:2004-03-12 Online:2004-07-20 Published:2015-09-09
Contact: 朱燕娟（1958－）女硕士副教授主要从事纳米材料制备与应用及非线性物理研究． E-mail:tczyj＠jnu.edu.cn
About author:朱燕娟（1958－）女硕士副教授主要从事纳米材料制备与应用及非线性物理研究．

摘要/Abstract

摘要： 提出一种统一的求解非线性演化方程孤波解的双曲函数法并利用这种方法求出了组合 KdV-mKdV 方程的钟状孤波解和激波状孤波解．作为特例可以给出 mKdV 方程的两类孤波解而且还给出了 KdV 方程的钟状孤波解．双曲函数法是利用非线性波动方程孤波解的局部性特点将方程的孤波解表示为双曲函数的多项式从而将非线性波动方程的求解问题转化为非线性代数方程组的求解问题．因此双曲函数法是一种简单而实用的方法．

关键词: 非线性演化方程, 孤波解, 双曲函数法, 组合 KdV-mKdV 方程

Abstract: A united hyperbolic function method to find the solitary wave solutions to nonlinear evolution equations was proposedand two kinds of solitary wave solutions to the combined KdV-mKdV equation were obtained by this method．As a special exampletwo kinds of solitary wave solutions to the mKdV equation can be obtainedand the bel- lshaped solution to the KdV equation was also given．The proposed method is based on the fact that the solitary wave solutions are essentially of a localized nature．In this methodthe solitary wave solutions to a nonlinear wave equation are denoted as the polynomials of hyperbolic functionsand the nonlinear wave equation is changed into nonlinear alge-braic equations．So the hyperbolic function method is simple and effective when used to study the solitary wave solu-tions of the nonlinear evolution equation．

Key words: nonlinear evolution equation, solitary wave solution, hyperbolic function method, combined KdV-mKdV equation

朱燕娟. 用双曲函数法求KdV- mKdV方程的钟状孤波解和激波状孤波解[J]. 华南理工大学学报(自然科学版), 2004, 32(7): 78-80.

Zhu Yan-juan. Two Kinds of Solitary Wave Solutions to the KdV-mKdV Equation Obtained by Hyperbolic Function Method[J]. Journal of South China University of Technology(Natural Science Edition), 2004, 32(7): 78-80.