Research On Analytical Solutions Of Two Classes Nonlinear Partial Differential Equations

Nonlinear partial differential equation(NLPDE)can simulate complex nonlinear phenomenons and solve practical problems we may encounter in different fields of nonlinear science.Currently,NLPDE has been a significantly hot field.This dissertation studies various solitary wave solutions of two kinds of nonlinear partial differential equation(s),and applies computer softwares,including Mathematica,Matlab to draw the images of these solutions.In addition,the dynamical properties and physical significance of these solutions are analyzed and discussed in details.The overall structures of the paper are arranged as follows:In Chapter 1,the research background is reviewed briefly,and the main methods used in the dissertation are introduced.In Chapter 2,we mainly study the space-time fractional Boussinesq couple system,which is a very important couple system,usually used to simulate nonlinear shallow water surface waves.We get the new exact solutions of the equations by modified auxiliary equation method,including(duck)periodical solutions and trigonometric solutions.Additionally,we transform the equations into the form of a planar system,determine all the bifurcation conditions of the system,and deduce the phase portraits of it,from which we get different new exact solutions of fractional Boussinesq equations,such as Jacobian elliptic function solutions.In Chapter 3,we mainly study the(3+1)-dimensional extended quantum Zakharov-Kuznetsov equation.Firstly,the generalized trigonometric function solutions and new traveling wave solutions of this equation are solved by(G’/G)-expansion method and Sech-Tanh expansion method.Then,the Adomain decomposition method is used to verify the accuracy of the two methods.In Chapter 4,we summarize the differences between this research and the existing ones from the perspectives of objects,methods and achievements.The inadequacies of the study are pointed out and the potential directions in future are analyzed.