Abstract and Applied Analysis
Volume 2012 (2012), Article ID 489043, 11 pages
http://dx.doi.org/10.1155/2012/489043
Research Article

The Bäcklund Transformations and Abundant Exact Explicit Solutions for a General Nonintegrable Nonlinear Convection-Diffusion Equation

Yong Huang1 and Yadong Shang2

1School of Computer Science and Educational Software, Guangzhou University, Guangzhou 510006, China
2School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received 25 October 2011; Accepted 14 November 2011

Academic Editor: Shaher M. Momani

Copyright © 2012 Yong Huang and Yadong Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Bäcklund transformations and abundant exact explicit solutions for a class of nonlinear wave equation are obtained by the extended homogeneous balance method. These solutions include the solitary wave solution of rational function, the solitary wave solutions, singular solutions, and the periodic wave solutions of triangle function type. In addition to rederiving some known solutions, some entirely new exact solutions are also established. Explicit and exact particular solutions of many well-known nonlinear evolution equations which are of important physical significance, such as Kolmogorov-Petrovskii-Piskunov equation, FitzHugh-Nagumo equation, Burgers-Huxley equation, Chaffee-Infante reaction diffusion equation, Newell-Whitehead equation, Fisher equation, Fisher-Burgers equation, and an isothermal autocatalytic system, are obtained as special cases.