Exact Solutions For Two Kinds Of Integrable Systems

Soliton and (quasi-)periodic solutions are influential exact solutions for nonlinear equations. In this thesis, by using Hirota bilinear method, we mainly discuss the generalized nonlinear Schrodinger equations. The N-soliton solutions and quasi-periodic solutions in term of ellipticθfunc-tions are obtained. Recently, the sixth-order nonlinear wave equation have been attraction interest. The N-soliton solutions expressed in different forms and nonlinear superposition formulation are presented by using Hi-rota bilinear method and the Backlund transformation method.In the first chapter, historical origin together with some knowledge of soliton and periodic solutions are presented,In the second chapter, we first deduce the bilinear form of nonau-tonomous nonlinear Schrodinger equation in the bright case and obtain its N-soliton solutions, what's more, the quasi-periodic solutions in term of elliptic 9 functions are also driven.The third chapter is mainly focused on the higher-order nonlinear Schr-odinger equation. The N-soliton solutions and several quasi-periodic so-lutions are obtained by means of Hirota bilinear method and the identity of elliptic 9 functions.In the forth chapter, we first present the bilinear form and the N-soliton solutions of the KdV6 equation. Further, the Backlund transformation and modified Backlund transformation are work out. Finally, the N-soliton solutions in different forms and nonlinear superposition formulation are also obtained.The last chapter is the concluding remarks.