## Journal of Applied Mathematics

### Traveling Wave Solutions of the Nonlinear $(3+1)$-Dimensional Kadomtsev-Petviashvili Equation Using the Two Variables $({G}^{\prime }/G,1/G)$-Expansion Method

#### Abstract

The two variables $({G}^{\prime }/G,1/G)$-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 $({G}^{\prime }/G)$-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.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 560531, 8 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495279

Digital Object Identifier
doi:10.1155/2012/560531

Mathematical Reviews number (MathSciNet)
MR2965716

Zentralblatt MATH identifier
1251.65150

#### Citation

Zayed, E. M. E.; Hoda Ibrahim, S. A.; Abdelaziz, M. A. M. Traveling Wave Solutions of the Nonlinear $(3+1)$ -Dimensional Kadomtsev-Petviashvili Equation Using the Two Variables $({G}^{\prime }/G,1/G)$ -Expansion Method. J. Appl. Math. 2012 (2012), Article ID 560531, 8 pages. doi:10.1155/2012/560531. https://projecteuclid.org/euclid.jam/1355495279