The Solutions Of Some Nonlinear Mathematical Physical Equations And The Behavior Analysis

With the rapid development of nonlinear science,the nonlinear evolution equations in the field of natural science,especially in the field of physics,are becoming more and more abundant.Due to the diversity and complexity of nonlinear evolution equations,looking for the exact solutions of the nonlinear evolution equations is always a hot research topic.Nowadays,there are many scholars engaged in this field.In this thesis,the solutions of three cylindrical(spherical)nonlinear mathematical physics equations are derived and the behavior of solutions is discussed.In the second chapter,a similarity transformation between the cylindrical(spherical)nonlinear Schrodinger equation and the nonlinear Schrodinger equation with variable coefficients is derived;and then using G?G-expansion method,the exact solutions of the nonlinear Schrodinger equation with variable coefficients are obtained;lastly,the various exact solutions(including the decay mode solutions,rogue waves solutions)of cylindrical(spherical)nonlinear Schrodinger equation are obtained with the help of the similarity transformation and the solutions of the nonlinear Schrodinger equation with variable coefficients.In the third chapter,a similarity transformations between the cylindrical(spherical)Gardner equation with variable coefficients and a Gardner equation with constant coefficients is derived,and the exact solutions(including the decay mode solutions)of the cylindrical(spherical)Gardner equation can be expressed by the solutions of Gardner equation with constant coefficients.In the fourth chapter,a similarity transformation between the cylindrical(spherical)Davey-Stewartson equations and the Davey-Stewartson equations with constant coefficients,and the corresponding constraint conditions for the coefficents of cylindrical(spherical)Davey-Stewartson equations are derived;using the similarity transformation and the rational solutions of Davey-Stewartson equations,the various exact solutions(the rational solutions)of two special cylindrical(spherical)DaveyStewartson equations can be obtained.Finally,the figures of the solutions are obtained using MATLAB,and the behavior of the solutions are studied.