With Five Items Nonlinear Schr (?) Dinger Equation Differential Decomposition Of The Long Time Behavior

Five times term Schrodinger equation with weakly damped is considered in this paper. with Dirichlet boundary condition and initial conditions WhereΩ= (0, L),α> 0,γ> 0, g∈L2(Ω).French mathematician R.Temam once said:"The study of nonlinear dynamics, is a fascinating question which is at the very heart of the understanding of many important problems of the natural sciences." In this paper,Nonlinear Schrodinger equation with weakly damped and five times term are studied.In the first chapter of this paper, we introduce brief about nonlinear dynamical system,background of Schrodinger equation and domestic and international research results are intro-duced. In the second chapter, some notions and lemmas which can be used follow-ing are introduced. In the third chapter, we direct at the character of Schrodinger equation with damped structuring fully different scheme firstly; then, the existence and uniqueness of solution of fully different scheme are proved by Leray-Schauder fix point theorem.Finally,the dynamical properties of a class of finite difference scheme are analysed.The stability of the differece scheme and the error estimate of the difference solution are obtained in the dynamics system,and existence of attractor is proved.