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

Zhaosheng Feng; Qingguo Meng

doi:10.3934/dcdsb.2007.7.285

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2007, Volume 7, Issue 2: 285-291. Doi: 10.3934/dcdsb.2007.7.285

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

Zhaosheng Feng^1, and
Qingguo Meng²

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

Received: August 31, 2006

Revised: October 31, 2006

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 13P10, 35Q53; Secondary: 34C05.

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

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