Abstract
The two variables -expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear -dimensional Kadomtsev-Petviashvili equation. This method can be considered as an extension of the basic -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.
Highlights
In the recent years, investigations of exact solutions to nonlinear PDEs play an important role in the study of nonlinear physical phenomena
The key idea of the original G /G -expansion method is that the exact solutions of nonlinear PDEs can be expressed by a polynomial in one variable G /G in which G G ξ satisfies the second ordinary differential equation G ξ λG ξ μG ξ 0, where λ and μ are constants
The key idea of the two variables G /G, 1/G -expansion method is that the exact traveling wave solutions of Journal of Applied Mathematics nonlinear PDEs can be expressed by a polynomial in the two variables G /G and 1/G, in which G G ξ satisfies a second order linear ODE, namely, G ξ λG ξ μ, where λ and μ are constants
Summary
Investigations of exact solutions to nonlinear PDEs play an important role in the study of nonlinear physical phenomena. The key idea of the two variables G /G, 1/G -expansion method is that the exact traveling wave solutions of Journal of Applied Mathematics nonlinear PDEs can be expressed by a polynomial in the two variables G /G and 1/G , in which G G ξ satisfies a second order linear ODE, namely, G ξ λG ξ μ, where λ and μ are constants The degree of this polynomial can be determined by considering the homogeneous balance between the highest order derivatives and nonlinear terms in the given nonlinear PDEs, while the coefficients of this polynomial can be obtained by solving a set of algebraic equations resulted from the process of using the method. Similar to Step 4, substitute 2.12 into 2.11 along with 2.2 and 2.6 for λ > 0 or 2.2 and 2.8 for λ 0 , we obtain the exact solutions of 2.11 expressed by trigonometric functions or by rational functions , respectively
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
