Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="(" close=")"> <mrow> <msup> <mrow> <mi>G</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mo>/</mo> <mi>G</mi> </mrow> </mfenced> </math>-Expansion Method

In this investigation, the exact solutions of variable coefficients generalized Zakharov-Kuznetsov (ZK) equation and Gardner are studied with help an extended G ′ / expansion method. The main objective study is to establish closed-form dynamics analytical ZK equation. govern behavior nonlinear wave phenomena in presence magnetic field plasma dynamics, turbulence, bottom topography, quantum theory. We construct innovative models under consideration using various computing tools a recently developed id="M3"> technique. id="M4"> technique well-defined simple which based on initial assumed polynomial id="M5"> . derived for both equations hyperbolic, trigonometric, rational functions. obtained have shock/kink waves multisoliton, depict dynamical representations acquired through three-dimensional surface plots contour plots.