Solitonic, super nonlinear, periodic, quasiperiodic, chaotic waves and conservation laws of modified Zakharov-Kuznetsov equation in transmission line

Abstract

In this paper, modified Zakharov-Kuznetsov (mZK) equation is taken into consideration. Diverse variety of solitonic structures are computed by using extended algebraic method. Sufficient conditions for the existence of the computed solutions are presented. Then, Galilean transformation is utilized to transform the considered model in the planer dynamical system. All possible forms of phase portraits with respect to the parameters are plotted. Moreover, we utilized the numerical techniques to find out the nonlinear periodic structures of the discussed model and results are shown graphically. Moreover, after deploying an extrinsic periodic force the effect of frequency is observed then sensitive analysis is applied for different initial value problems to analyze the quasiperiodic and chaotic behaviour. In addition to this, Lie point symmetries and their corresponding conservation laws are reported at the end.