Modified Kudryashov method and its applications to the (2+1)-dimensional cubic Klein-Gordon and (3+1)- dimensional Zakharov-Kuznetsov equations (original) (raw)
Related papers
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.
PloS one, 2013
The generalized and improved (G'/G)-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.
The Improved (𝐺′/𝐺)-Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation
Journal of Applied Mathematics, 2012
we apply the improved(G′/G)-expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition,G″+λG′+μG=0together withb(α)=∑q=−wwpq(G′/G)qis employed in this method, wherepq(q=0,±1,±2,…,±w),λandμare constants. Moreover, the obtained solutions including solitons and periodic solutions are described by three different families. Also, it is noteworthy to mention out that, some of our solutions are coincided with already published results, if parameters taken particular values. Furthermore, the graphical presentations are demonstrated for some of newly obtained solutions.