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Abstract
A new extended (G ' =G)-expansion method is presented in this paper to construct more general type and new traveling wave solutions of nonlinear partial differential equations. To illustrate the novelty and advantage of the proposed method, we solve the (3+1)-dimensional Jimbo-Miwa equation. Abundant exact traveling wave solutions of this equation is ob- tained, which successfully recover most of the previously published solutions. Many of those solutions are found for the first time. Furthermore, the results reveal that the proposed method is very elementary, effective and can be used for many other nonlinear partial differential equations.
Highlights
Many complex real world problems in nature are due to nonlinear phenomena
Seeking the exact solutions of nonlinear partial differential equations plays an significant role, when we want to understand the physical mechanism of the phenomena such as the wave phenomena observed in fluid dynamics [7,14], plasma and elastic media [8,13]
The objective of this article is to apply the proposed method to construct the exact solutions for nonlinear partial differential equations in mathematical physics via the (3+1)-dimensional Jimbo-Miwa equation
Summary
Many complex real world problems in nature are due to nonlinear phenomena. Nonlinear processes are one of the biggest challenges and not easy to control because the nonlinear characteristic of the system abruptly changes due to some small changes of valid parameters including time. Seeking the exact solutions of nonlinear partial differential equations plays an significant role, when we want to understand the physical mechanism of the phenomena such as the wave phenomena observed in fluid dynamics [7,14], plasma and elastic media [8,13]. A number of prominent mathematicians and physicists have devoted considerable efforts on this interesting area of research to obtain exact solutions of nonlinear partial differential equations using symbolical computer programs such as Maple, Matlab, Mathematica that facilitate complex and tedious algebraical computations. Applying the (G′/G)-expansion method, many authors successfully obtained more exact traveling wave solutions to a large number of nonlinear partial differential equations like [4, 16]. The objective of this article is to apply the proposed method to construct the exact solutions for nonlinear partial differential equations in mathematical physics via the (3+1)-dimensional Jimbo-Miwa equation.
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