The Improved ( G ’ / G ) -Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation

Abstract

we apply the improved $(G^{\prime }/G)$-expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition, $G^{″}+\lambda G^{\prime }+\mu G=0$ together with $b(\alpha )={\sum }_{q=-w}^w{p}_q{(G^{\prime }/G)}^q$ is employed in this method, where $p_q(q=0,\pm 1,\pm 2,\dots ,\pm$ $w)$, $\lambda$ and $\mu$ are 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.