Traveling Wave Solutions And Dynamic Analysis Of Three Nonlinear Evolution Equations With Variable Coefficients

Since the 19 th century,the nonlinear evolution equation has been widely used in physics,mechanics,plasma physics,condensation physics,atmospheric physics,fluid mechanics and other fields.The exploration of the exact solutions of the equation is conducive to understand the intrinsic nature of the development of things.Due to the complexity of the equation,there is still no unified method to solve the nonlinear evolution equation up to now.The development of computer technology has brought a whole new energy to solve nonlinear partial differential equations and nonlinear scientific research,so it becomes one of the main means to study the nonlinear evolution equation.Based on the unified method,the generalized unified method,combined with the improved F-expansion method and the modified Kudryashov method,this paper studies the solving problems of three types of nonlinear evolution equations.The specific contents are as follows:(i)The generalized(3+1)-dimensional variable coefficients Kadomtsev-Petviashvili equation is solved by the unified method and the generalized unified method.Firstly,the single soliton rational solutions of the equation are obtained by using the unified method,including elliptic traveling wave rational solution and solitary wave rational solution.Then,the generalized unified method is used to obtain the double solitons rational solution of the equation and the graphs of these solutions are drawn with appropriate parameters.(ii)The traveling wave solutions of the(2+1)-dimensional generalized variable coefficients Zakharov-Kuznetsov equation are solved by the unified method,the improved F-expansion method and the modified Kudryashov method.Firstly,the polynomial solutions and rational solutions of the equation are obtained by using the unified method.The polynomial solutions include the solitary wave solution,the soliton wave solution and the elliptic wave solution.The rational solutions include the periodic type rational solution and the soliton type rational solution.Then the improved F-expansion method is used to obtain hyperbolic trigonometric function solutions,trigonometric function solutions and rational solutions of the equation.Finally,the traveling wave solution of the equation is obtained by using the modified Kudryashov method.(iii)The complex wave solutions of the(3+1)-dimensional variable coefficients coupled nonlinear Schr¨odinger equation are solved by the unified method,the improved F-expansion method and the modified Kudryashov method.Firstly,the polynomial solutions of the equation,including complex solitary wave solutions,complex soliton wave solutions and complex elliptic wave solutions,are obtained by using the unified method.The graphs of these solutions are drawn with appropriate parameters.Then the complex hyperbolic trigonometric function solutions,complex trigonometric function solutions and complex rational solutions of the equation are obtained by using the improved F-expansion method.Finally,the complex wave solution of the equation is obtained by using the modified Kudryashov method.