强非线性广义 Boussinesq 方程孤波解的波形分析及求解

数学物理学报

强非线性广义 Boussinesq 方程孤波解的波形分析及求解

张卫国; 陶涛

上海理工大学理学院上海 200093

收稿日期:2005-10-08 修回日期:2007-08-08 出版日期:2008-02-25 发布日期:2008-02-25
通讯作者: 张卫国
基金资助:
国家自然科学基金(10371023)、上海市重点学科项目(T0502)和上海
市教委科技发展基金项目(07ZZ83)资助

Analysis of Solitary-wave Shape and Solutions of the Generalized

Strong Nonlinear Boussinesq Equation

zhangWeiguo; Tao Tao

College of Science, University of Shanghai for Science and Technology, Shanghai 20009

Received:2005-10-08 Revised:2007-08-08 Online:2008-02-25 Published:2008-02-25
Contact: zhangWeiguo

摘要/Abstract

摘要： 上海理工大学理学院\quad 上海 200093该文建立了强非线性广义 Boussinesq 方程的耗散项、波速、渐进值与波形函数的导数之间的关系.利用适当变换和待定假设方法,作者求出了上述广义 Boussinesq 方程的扭状或钟状孤波解,还求出了以前文献中未曾提到过的余弦函数的周期波解.进一步给出了波速对波形影响的结论,即:``好''广义 Boussinesq 方程的行波当波速
由小变大时,波形由钟状孤波变成余弦函数周期波解;``坏''广义 Boussinesq 方程的行波当波速由小变大时,波形由余弦函数周期波解变成钟状孤波.

关键词: 强非线性, Boussinesq 方程, 波形分析, 孤波解, 周期函数波解.

Abstract: In this paper, the relations among dissipation term, speed of wave, asymptotic value and wave shape are established for generalized strong nonlinear Boussinesq equation. Their kink or bell shape solitary-wave
solutions are obtained by proper transformation and undetermined assumption method. The authors also obtain the periodic wave solutions of cosine function for the generalized Boussinesq equation without dissipation term, which have not been reported before. Moreover, a conclusion with respect to wave speed's influence on wave shape is shown, i.e., for ``good'' Boussinesq equation travalling wave solution changes to cosine periodic wave solution from bell shape
solitary-wave solution as wave speed varies from small to large; for ``bad'' Boussinesq equation travalling wave solution changes to bell shape solitary-wave solution from cosine periodic wave solution as wave speed varies from small to large.

Key words: Strong nonlinear, Boussinesq equation, Analysis of wave shape,
Solitary-wave solution, Cosine periodic wave solution

中图分类号:

35Q20

张卫国; 陶涛.

强非线性广义 Boussinesq 方程孤波解的波形分析及求解

[J]. 数学物理学报, 2008, 28(1): 86-92.

zhangWeiguo; Tao Tao. Analysis of Solitary-wave Shape and Solutions of the Generalized

Strong Nonlinear Boussinesq Equation[J]. Acta mathematica scientia,Series A, 2008, 28(1): 86-92.

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