The Research Of Solving The Solutions Of Some Nonlinear Evolution Equations And The Property Of The Solutions

With the development of science and technology,a large number of accurate mathematical models of constant(variable)coefficient nonlinear evolution equations(groups)have been established in many scientific fields,and soliton solutions have been obtained.In order to understand the practical significance of this kind of mathematical model more deeply,it is meaningful to construct new exact solutions of constant(variable)coefficient nonlinear evolution equations(groups)and study some related issues.Recently,many effective methods have been proposed in the field of solving nonlinear evolution equations(groups)based on computer algebraic systems.For example: homogeneous balance method,hyperbolic tangent function method,Jacobi elliptic function expansion method,auxiliary equation method and Hirota bilinear method.In this paper,based on the auxiliary equation method,and the method of combining function transformation and auxiliary equation method is given.and the new complexion solutions composed of multiple functi-ons of deformation Boussinesq equation group with asymmetric variable coefficients,Novikov equation group with coupled variable coefficient and mKdV equation are constructed.In addition,based on the Hirota bilinear method,multiple soliton solutions and rouge wave solutions of(3+1)-dimensional high-dimensional soliton equation with constant coefficient and(3+1)-dimensional K-P equation with variable coefficient are constructed.In the first chapter,the development of the soliton theory and several methods of solving the solutions of the nonlinear evolution equations are reviewed,and the main work of this paper are encapsulated.In the second chapter,by using the relevant conclusions of two common auxiliary equations,the new complexion solutions composed of multiple functions of deformation Boussinesq equation group with asymmetric variable coefficients and Novikov equation group with coupled variable coefficient are constructed,and the properties of the solutions are studied by using computation system Mathematica.1.By using the method of combining two kinds of ordinary differential equations with function transformation,some new infinite sequence complexion solutions consisting of exponential function,trigonometric function and rational function of the deformation Boussinesq equation group with asymmetric variable coefficients are obtained,On this basis,the properties of complexion solutions are analyzed by using symbolic computing system Mathematica.2.By using the method of combining two auxiliary equations and function transformation,the complexion solutions of Novikov equation group with variable coefficient are obtained,which are composed of hyperbolic function,exponential function,trigonometric function and rational function.The new solutions include soliton-like solutions,double-soliton-like solutions and biperiodic-like solutions.In the third chapter,the method of combining two first class elliptic equations with function transformation is given,new infinite sequence complexion solutions of mKdV equation are obtained.Which include the new solutions of double-periodic and two-soliton are included.In addition,the properties of the solutions are analyzed by using the symbolic computation system Mathematica.In the fourth chapter,based on the Hirota bilinear method,the multiple soliton solutions and rouge wave solutions of(3+1)-dimensional high-dimensional soliton equation with constant coefficients and the(3+1)-dimensional K-P equation with variable coefficients are obtained.1.Step 1:By transformating logarithmic function,the(3+1)-dimensional high-dimensional soliton equation is transformed into the bilinear equation;Step 2: By using the series perturbation method,single soliton solution,double soliton solution and N-soliton solution of bilinear equation are solved;Step 3: Rouge wave solutions of(3+1)-dimensional high-dimensional soliton equation are constructed by combining generalized rational polynomial with heuristic method;Step 4: Analysing the properties of the solutions.2.Step 1: By using the Hirota bilinear method,the(3+1)-dimensional K-P equation with variable coefficients is simplified into bilinear form;Step 2: The rouge wave solutions are constructed by giving the function transformation of variable coefficients.In addition,the properties of solutions are analyzed by using symbolic computation system mathematica.