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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 657918, 5 pages
http://dx.doi.org/10.1155/2013/657918
Research Article

The General Traveling Wave Solutions of the Fisher Equation with Degree Three

1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China
3Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510420, China
4Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China
5School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 13 May 2013; Accepted 19 August 2013

Academic Editor: Ricardo Weder

Copyright © 2013 Wenjun Yuan et al. 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

We employ the complex method to research the integrality of the Fisher equations with degree three. We obtain the sufficient and necessary condition of the integrable of the Fisher equations with degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006), Guo and Chen (1991), and Ağırseven and Öziş (2010). Moreover, all are new general meromorphic solutions of the Fisher equations with degree three for . Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.