Bifurcation And Solutions Structure Of Three Nonlinear Evolution Equations

Abstract:The bifurcation and structure of solutions of Khokhlov-Zabolotiskaya-Kuznetsove equation,generalized(3+1)dimensional Kadomtsev-Petviashvili equation,(3+1)dimensional time fractional Kdv-Zakharov-Kuznetsov equation are analysed and constructed in this thesis.The method processes and results are presented as follows.Combining with the integrated fractional dervative and using the extended(G'/G)expan-sion method which add new auxiliary equation,the exact solutions of fractional Khokhlov-Zabolotskaya-Kuznetsov equation are constructed.The new exact solutions contain hyperbolic function solution,trigonometric function solution and rational function solution.Utilizing the ansatz method,the singular soliton solution,bright soliton solution and topo-logical soliton solution of(3+1)dimensional time fractional Kdv-Zakharov-Kuznetsov equa-tion are constructed.Secondly,the equation is transformed into planar dynamical system.By the bifurcation analysis,we obtain the phase portraits of the dynamical system,which reveal that there are saddle point,center point and degenerate saddle point,and different orbit.In-tegrating along the orbit,we obtained exact solutions,which include periodic solutions and singular wave solutions.The singular solution of Kadomtsev-Petviashvili equation is obtained by the ansatz method.Besides,the bifurcation analysis of the planar dynamical system is investigated,The phase portraits of the planar dynamical system is obtained.Furthermore,by the bifurcation analysis,we obtained exact solutions,which include periodic solutions and singular wave so-lutions.