Bifurcation Of Traveling Wave Solutions Of A Class Of Zakharov-Kuznetsov Equation

The traveling wave solution of the nonlinear wave equation and the bifurcation of the dynamic system are an important part of the nonlinear science.The correspondence between the phase diagram trajectories of traveling wave equations and the nonlinear waves is the intermediate junction of two areas in the nonlinear science.Applying the progressive multiscale technique in two-dimensional space,the famous KdV equation is extended to the Zakharov-Kuznetsov equation.That is of great theoretical and practical significance to study the phenomenon of nonlinear fluctuation.In this paper,bifurcation of exact traveling wave solutions of(2+1)dimensional Zakharov-Kuznetsov equations,generalized Zakharov-Kuznetsov equations and modified Zakharov-Kuznetsov equations are investigated by using the plane dynamical system theory,the research contents of this dissertation are as follows:(1)The three kinds of partial differential equations are transformed into ordinary differential equations by traveling wave transformation,and the singular points of ordinary differential equations are analyzed.(2)By choosing different bifurcation parameter sets,the dynamical behavior of corresponding Hamiltonian system in different regions is analyzed,and the bifurcation diagram of phase diagram is obtained.(3)According to the elliptic integral method,the exact travelling wave solutions of three kinds of nonlinear equations are obtained,including periodic wave solutions,solitary wave solutions,kink wave solutions and anti kink wave solutions.Maple symbol calculation software is used to draw the corresponding waveform of the original system.