The Exact Solution Of Certain Types Of Soliton Equations

In this paper, based on the theory of many nonlinear evolution equations and soliton solution, I used the bilinear method,do some researches on soliton equations. Solved exact solutions of the model, at the same times multi-soliton solutions are also obtained.The first chapter, I introduce the theory of solitons history and development, then describe several nonlinear evolution equations solving method, and the application of these methods and development. At last, describes the background, the physical meaning and practical application of the nonlinear evolution equations with variable coefficients model.Chapter II, In the first part, introduces the definition of bilinear derived formula and the formula for the basic nature; the second part, the introduction of generalized fifth-order KdV equation, and its research status details, then uses bilinear method to solve the generalized fifth-order KdV equation's exact solutions (single soliton solutions, soliton solutions of two-and three-soliton solutions), and extended to the N-soliton solution for further. At last, drawn images soliton by computer.The third chapter is based on the second chapter, move forward a single step by using the bilinear method to solve a (2+1)-dimensional model equation. Extended the dimensional from (1+1)-dimensional to (2+1)-dimensional for the new model.We also got the exact solutions, and drew the soliton graphs.Chapter IV, I summarizes the results of this paper, described my views and experiences in the study of soliton equations.