时滞KdV-Burgers方程的行波解  

Travelling Wave Solutions for Time-delayed KdV-Burgers Equation

作　　者：李二强[1] 李灵晓[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2012年第3期66-69,74,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省国际合作交流基金项目(094300510050);河南省教育厅自然科学研究计划项目(2011B110013)

摘　　要：利用流量松弛方法导出了时滞KdV-Burgers方程,并利用(1/G)-展开法,求得时滞KdV-Burgers及KdV-Burgers方程的行波解。结合所求得的解,对时滞KdV-Burgers方程行波约化后所得的常微分方程组(ODEs)进行了定性分析。研究表明:当时间特征常数τ与行波波速c的平方之积等于耗散系数α(即τc2=α)时,时滞KdV-Burgers方程出现了椭圆余弦波解和钟状孤波解,而KdV-Burgers方程没有此类解。另外,时滞的存在还影响到孤立波的振幅和波宽。The time-delayed KdV-Burgers equation was derived by using the flux relaxation method.The travelling wave solutions of the time-delayed KdV-Burgers equation and the KdV-Burgers equation were obtained by the (1/G)-expansion method.According to these solutions,the qualitative analysis of the nonlinear ODEs reduced by using traveling wave variable of the time-delayed KdV-Burgers equation was given.When the delayed constant timed by the square of the traveling speed c equals the dissipative coefficient,there exist bell solitary wave and cnoidal wave solutions in the time-delayed KdV-Burgers equation,while the KdV-Burgers equation has no the two types solutions.The existence of time delaying affects the amplitude and the wave width of the solitary waves.

关 键 词：时滞KdV-Burgers方程 流量松弛方法 行波解 齐次平衡 定性分析 

分 类 号：O175.29[理学—数学]