Abstract:. In this talk, first we survey some recent advances in the study of traveling solitary waves of the Burgers-Korteweg-de Vries equation and some comments are given. Then, 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 involves the Lie group analysis. 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 arbitrary velocity is obtained accordingly. Finally, we generalize our study to a Burgers-Korteweg de-Vries-type equation with higher-order nonlinearities。

Vita: Dr. Zhaosheng Feng obtained his Ph.D in Mathematics from Texas A&M University, 2004. He is now an assistant professor in the mathematics department of University of Texas-Pan American. Dr. Feng's research interests include applied analysis, nonlinear differential equations (ODEs, PDEs and NLWEs), dynamical systems, mathematical physics and computational methods.

清华大学周培源应用数学研究中心

秘　书：　唐　琳

TEL：62797063