Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

Abstract

In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized$\left(G^{\prime }/G\right)$expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized$\left(G^{\prime }/G\right)$expansion technique. The extended generalized$\left(G^{\prime }/G\right)$expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of$\left(G^{\prime }/G\right)$. The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.