The Study On Exact Solutions Of Two Kinds Of Evolution Equations

At present,nonlinear scientific research has become one of the focuses of scientific research.In the field of different research,we encounter different types of nonlinear equations,and how to solve these different types of nonlinear equations has become the key of this field.In recent years,with the extensive application of mathematical mechanization,a large number of new methods have been developed to solve the nonlinear equations,which have effectively promoted the development of nonlinear systems.In this paper,we study the exact solutions of two kinds of equation,namely the nonlinear variable coefficients Sharma-Tasso-Olver(STO)equation and the fractional nonlinear Klein-Gordon equation.This paper is divided into five chapters.In the first chapter,we mainly introduce the research background of variable coefficients nonlinear equations and fractional partial differential equations,and the existing research methods.Finally,the contents of each chapter are given.In the second chapter,the background of the STO equation and the existing methods and results are introduced firstly.Secondly,the symmetric analysis of the variable coefficients STO equation is carried out based on the Lie symmetry method,and the symmetric reduction equations are obtained.Finally,the tanh method,the simplest function method and the power series solution method are used to obtain the exact solutions of all the reduction equations,and then we obtain the exact solutions of the variable coefficients STO equation.In the third chapter,the variable coefficients STO equation is discussed again by using the generalized (G’/G)-expansion method,and new exact solutions which are different from the result of the second chapter are obtained.In the fourth chapter,the exact solutions of the improved Riemann-Liouville fractional nonlinear Klein-Gordon equation are obtained by using the complex transformation with three different methods.Chapter five summarizes the full text.