| 时滞KdV-Burgers方程的行波解 |
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| 引用本文： | 李二强,李灵晓.时滞KdV-Burgers方程的行波解[J].河南科技大学学报(自然科学版),2012,33(3):66-69,74,113. |
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| 作者姓名： | 李二强 李灵晓 |
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| 作者单位： | 河南科技大学数学与统计学院,河南洛阳,471003 |
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| 基金项目： | 河南省国际合作交流基金，河南省教育厅自然科学研究计划项目 |
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| 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。
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| 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 |
Travelling Wave Solutions for Time-delayed KdV-Burgers Equation |
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| LI Er-Qiang,LI Ling-Xiao.Travelling Wave Solutions for Time-delayed KdV-Burgers Equation[J].Journal of Henan University of Science & Technology:Natural Science,2012,33(3):66-69,74,113. |
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| Authors: | LI Er-Qiang LI Ling-Xiao |
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| Institution: | (Mathematics & Statistics School,Henan University of Science & Technology,Luoyang 471003,China) |
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| Abstract: | 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. |
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| Keywords: | Time-delayed KdV-Burgers equation Flux relaxation method Traveling wave solution Homogeneous balance Qualitative analysis |
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