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Journal of Applied Mathematics
Volume 2012, Article ID 560531, 8 pages
Research Article

Traveling Wave Solutions of the Nonlinear ( 3 + 1 ) -Dimensional Kadomtsev-Petviashvili Equation Using the Two Variables ( 𝐺 / 𝐺 , 1 / 𝐺 ) -Expansion Method

Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Received 20 June 2012; Revised 30 July 2012; Accepted 31 July 2012

Academic Editor: Turgut Öziş

Copyright © 2012 E. M. E. Zayed 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.


The two variables ( 𝐺 / 𝐺 , 1 / 𝐺 ) -expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear ( 3 + 1 ) -dimensional Kadomtsev-Petviashvili equation. This method can be considered as an extension of the basic ( 𝐺 / 𝐺 ) -expansion method obtained recently by Wang et al. When the parameters are replaced by special values, the well-known solitary wave solutions and the trigonometric periodic solutions of this equation were rediscovered from the traveling waves.