Long-time Behavior Of Fourier Spectral Approximation To Nonlinear KdV-Schr(?)dinger Equation

Recently, more and more attentions are paid to the study of nonlinear evolution equations with weakly damped. Mostly, the equations' exact solution can't be gotten, all we can do is to investigate the equations' properties through their numerical simulations.The main purpose of this work is to investigate the long-time behaviors of Fourier spectral approximation to nonlinear KdV-Schrodinger equation.Firstly, we introduce some orthogonal systems, on which we develop some results of projected operator, and several basic inequalities.Secondly, for the equation considered in this paper, we constitute Fourier spectral scheme and relevant priori estimates. Following which, we give the error estimates between the approximate solution and the exact solution.At last, we prove the existence and convergence of the attractor.