The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivi...The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré 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.展开更多
基金This work was supported by US National Science Foundation(Grant No.CCF-0514768)partly supported by UTPA Faculty Research Council(Grant No.119100)
文摘The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré 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.
