With Weak Damping Of Nonlinear Schr (?) Dinger Equation For The Dynamical Properties Of Fully Discrete Spectral Scheme And A Long Period Of Stability And Convergence

In this paper,the nonlinear Schrodinger equation with weakly damped, together with appropriate boundary and periodic conditions is considered.According to the need of problem,we make two assumptions of g(s) besides the assumption conditions of references [13]. we construct the full discrete Fourier Spectral scheme and prove the existence and uniqueness of the solution of the Spectral scheme.Firstly ,let us put the discrete scheme in the framework of dissipa-tive dynamical systems.we abtain the long-time priori estimate for the solution of the discrete system and the stability and convergence of the Spectral scheme, we also prove the existence of an absorbing set BN in the Snn,T In this section we prove attractor AN,T existence on discrete systemes {(SN,T)n}n>0.At last ,let us put the discrete scheme in the nonautonomouse case, we obtain the long-time priori estimate for the solution of the Spectral scheme and the long-time error estimate . In this section,let us replace PNf by PNfn+1/2and finally we obtain the stability and convergence of the discrete Spectral scheme .