摘要
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.
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 travailing 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 travailing wave solution changes to bell shape solitary-wave solution from cosine periodic wave solution as wave speed varies from small to large.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2008年第1期86-95,共10页
Acta Mathematica Scientia
基金
国家自然科学基金(10371023)
上海市重点学科项目(T0502)
上海市教委科技发展基金项目(07ZZ83)资助
关键词
强非线性
BOUSSINESQ方程
波形分析
孤波解
周期函数波解
Strong nonlinear
Boussinesq equation
Analysis of wave shape
Solitary-wave solution
Cosine periodic wave solution.
