March  2007, 7(2): 285-291. doi: 10.3934/dcdsb.2007.7.285

Exact solution for a two-dimensional KDV-Burgers-type equation with nonlinear terms of any order

1. 

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541

2. 

Department of Mathematical Science, Tianjin University of Technology and Education, Tianjin 300222, China

Received  September 2006 Revised  November 2006 Published  December 2006

In this paper, we study a two-dimensional Burgers--Korteweg-de Vries-type equation with higher-order nonlinearities. A class of solitary wave solution is obtained by means of the Divisor Theorem which is based on the ring theory of commutative algebra. Our result indicates that the presentation of traveling wave solution in [J. Phys. A (Math. Gen.) 35 (2002) 8253--8265] is incorrect; an explanation as to why this is so is given.
Citation: Zhaosheng Feng, Qingguo Meng. Exact solution for a two-dimensional KDV-Burgers-type equation with nonlinear terms of any order. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 285-291. doi: 10.3934/dcdsb.2007.7.285
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