Burgers-Korteweg-de Vries equation and its traveling solitary waves

被引：19

作者：

Feng, Zhao-sheng ^{[1
]}

Meng, Qing-guo

机构：

[1] Univ Texas, Dept Math, Edinburg, TX 78541 USA

[2] Tianjin Univ Technol & Educ, Dept Math Sci, Tianjin 300222, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2007年 / 50卷 / 03期

基金：

美国国家科学基金会;

关键词：

traveling wave; autonomous system; Lie group; infinitesimal generator; Burgers-KdV equation; Painleve analysis;

D O I：

10.1007/s11425-007-0007-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincare phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivial bell-profile traveling solitary waves, nor periodic waves. In the present paper, we show two approaches for the study of traveling solitary waves of the Burgers-Korteweg-de Vries equation: one is a direct method which involves a few coordinate transformations, and the other is the Lie group method. Our study indicates that the Burgers-Korteweg-de Vries equation indirectly admits one-parameter Lie groups of transformations with certain parametric conditions and a traveling solitary wave solution with an arbitrary velocity is obtained accordingly. Some incorrect statements in the recent literature are clarified.

引用

页码：412 / 422

页数：11

共 52 条

[31] A NON-LINEAR EQUATION INCORPORATING DAMPING AND DISPERSION [J].