Research On Some Nonlinear Wave Equations By The First Integral Method

In this paper, we introduce the basic idea of the first integral method and its revisionprocesses in detail, and apply the first integral method in the aspect of exactly solving thenonlinear partial diferential equations with algebraic method by Fan Engui. In the processof solving the problem, the first integral method avoids the complicated calculation. Withthe algebraic method, discuss the parameters in detail and obtain more abundant explicitexact particular solutions than before. These solutions include the solitary wave solu-tions of rational function, the solitary wave solutions of kink-shaped, the solitary wavesolutions of bell-shaped, singular traveling wave solutions, the periodic wave solution-s of triangle function, Jacobi elliptic function solutions and Weierstrass elliptic functionperiodic solutions.This paper is organized as follows: chapter one summarizes some main methods offinding the exact solutions of the nonlinear partial diferential equations brought forwardfrom home and abroad, presents the background and their application operating processof the first integral method, and introduces the aim of research and the primary contentsof this paper briefly. From chapter two to chapter five, we apply the first integral methodto the equations, and obtains abundant explicit exact solutions. It include some new solu-tions, such as the solitary wave solutions of bell-shaped, Jacobi elliptic function solutionsand Weierstrass elliptic function periodic solutions.Then compare these solutions to the currently solutions.Finally, we make a summary of this paper and look ahead of research orientation infuture.