The Method Of Shoving The Nonlinear Evolution Equation With Constant Coefficients And Variable Coefficients

Currently, scientists have proposed a number of methods for solving nonlinear evolution equations. Most of them, however, can only be use to solve equations with constant coefficients. Now, we study the method of solving the nonlinear evolution equation with constant coefficients and variable coefficients in this thesis. In other words, we improve previous proposed methods for solving the equations with constant coefficients, in order to make them equally effective in solving the equations with variable coefficients.Firstly, we introduce several important concepts of nonlinear evolution equa-tions and describe the methods for solving these equations. Then we focus on the origin and physics of the equations which we will study in this thesis.Secondly, we expand the generalized Riccati equation rational expansion method and use it to solve the generalized Burgers-Fisher equation with variable co-efficients. After calculation and deduction, we propose six theorems on the solutions of the equation. The results show that improved the generalized Riccati equation rational expansion method for solving nonlinear evolution equations is valid.Thirdly, we obtain many solutions of KdV-Burgers-Kuramoto equation, KdV-Burgers equation and Kuramoto-Sivashinsky equation by using the exp-function method. Using hyperbolic function transformation, these solutions are simplified. We also obtain the solutions of KdV-Burgers-Kuramoto equation with variable co-efficients by using the improved exp-function method which has been proposed by other scientists. Through the solution process we found that if you want to obtain the new solutions, you must reserve the highest order terms and the lowest order terms of the solution's form. The middle terms, however, can be reduced.Finally, we make a summary of the thesis and give an outlook of the future research direction.