BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

doi:10.1016/S0252-9602(14)60061-8

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 941-959.doi: 10.1016/S0252-9602(14)60061-8

BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

张卫国*, 刘强, 李正明, 李想

School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China|Department of Mathematics and Information Science, the College of Zhengzhou Light Industry, Zhengzhou 450002, China|Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

收稿日期:2013-05-09 修回日期:2013-07-17 出版日期:2014-05-20 发布日期:2014-05-20
作者简介:张卫国|zwgzwm@126.com|zwgzwm@sohu.com
基金资助:
The first author is supported by National Natural Science Foundation of China (11071164), Innovation Program of Shanghai Municipal Education Commission (13ZZ118), and Shanghai Leading Academic Discipline Project (XTKX2012).

BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

ZHANG Wei-Guo*, LIU Qiang, LI Zheng-Ming, LI Xiang

School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China|Department of Mathematics and Information Science, the College of Zhengzhou Light Industry, Zhengzhou 450002, China|Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2013-05-09 Revised:2013-07-17 Online:2014-05-20 Published:2014-05-20
About author:ZHANG Wei-Guo|zwgzwm@126.com|zwgzwm@sohu.com
Supported by:
The first author is supported by National Natural Science Foundation of China (11071164), Innovation Program of Shanghai Municipal Education Commission (13ZZ118), and Shanghai Leading Academic Discipline Project (XTKX2012).

摘要/Abstract

摘要：

This article studies bounded traveling wave solutions of variant Boussinesq equa-tion with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and gen-eral shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r* which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r| ≥ r*; while they appear as damped oscillatory waves if |r| < r*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory so-lutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions (u(ξ), H(ξ)). Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.

关键词: Variant Boussinesq equation with dissipation term, shape analysis, bounded traveling wave solution, error estimate, dissipation effect

Abstract:

Key words: Variant Boussinesq equation with dissipation term, shape analysis, bounded traveling wave solution, error estimate, dissipation effect

中图分类号:

35G20

张卫国, 刘强, 李正明, 李想. BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT[J]. 数学物理学报(英文版), 2014, 34(3): 941-959.

ZHANG Wei-Guo, LIU Qiang, LI Zheng-Ming, LI Xiang. BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT[J]. Acta mathematica scientia,Series B, 2014, 34(3): 941-959.

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BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

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