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

作者：Feng Zhao sheng^*; Meng Qing guo

来源：Science in China Series A-Mathematics, 2007, 50(3): 412-422.

DOI：10.1007/s11425-007-0007-6

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

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.

• 出版日期2007-3
• 单位天津职业技术师范大学