New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the ( 2 + 1 ) -Dimensional Evolution Equation

Abstract

The generalized Riccati equation mapping is extended with the basic $(G^{\prime }/G)$-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation $G^{\prime }(\eta )=w+uG(\eta )+v{G}^2(\eta )$ is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.