| Burgers-Korteweg-de Vries equation and its traveling solitary waves |
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| 作者姓名： | Zhao-sheng FENG & Qing-guo MENG |
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| 作者单位： | Zhao-sheng FENG & Qing-guo MENG Department of Mathematics，University of Texas-Pan American，Edinburg，TX 78541，USA Department of Mathematical Science，Tianjin University of Technology and Education，Tianjin 300222，China |
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| 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.
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| 关 键 词： | Painlevé analysis |
| 收稿时间： | 28 February 2006 |
| 修稿时间： | 26 October 2006 |
Burgers-Korteweg-de Vries equation and its traveling solitary waves |
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| Zhao-sheng FENG & Qing-guo MENG.Burgers-Korteweg-de Vries equation and its traveling solitary waves[J].Science in China(Mathematics),2007,50(3):412-422. |
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| Authors: | Zhao-sheng Feng Qing-guo Meng |
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| Institution: | 1. Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541, USA
2. Department of Mathematical Science, Tianjin University of Technology and Education, Tianjin 300222, China |
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| Abstract: | 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. |
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| Keywords: | traveling wave autonomous system Lie group infinitesimal generator Burgers-KdV equation |
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