Generalized and improved (G'/G)-expansion method for (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation (original) (raw)
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2013
The generalized and improved G0=Gð Þ-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple.
In this work, we established abundant traveling wave solutions for nonlinear evolution equations. The exp(( )) -expansion method was used to construct traveling wave solutions for nonlinear evolution equations. The traveling wave solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. This method is one of the powerful methods that appear in recent time for establishing exact traveling wave solutions of nonlinear partial differential equations. It is shown that the exp(( )) -expansion method is straightforward and effective mathematical tool for solving nonlinear evolution equations in mathematical physics and engineering.
Exact solutions of nonlinear evolution equations (NLEEs) play very important role to make known the inner mechanism of compound physical phenomena. In this paper, the new generalized (GG/′)-expansion method is used for constructing the new exact traveling wave solutions for some nonlinear evolution equations arising in mathematical physics namely, the (3+1)-dimensional Zakharov-Kuznetsov equation and the Burgers equation. As a result, the traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. This method is very easy, direct, concise and simple to implement as compared with other existing methods. This method presents a wider applicability for handling nonlinear wave equations. Moreover, this procedure reduces the large volume of calculations.
2013
In this article, the improved ()/G G ′-expansion method has been implemented to generate travelling wave solutions, where ()G ξ satisfies the second order linear ordinary differential equation. To show the advantages of the method, the (3+1)-dimensional Kadomstev-Petviashvili (KP) equation has been investigated. Higher-dimensional nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation. Also, in order to understand the behaviour of solutions, the graphical representations of some obtained solutions have been presented.