With Weak Damping Of The Korteweg-de Vries Equation Fourier Spectral Method

One-dimensional weakly damped Korteweg-de Vries equations is considered in the paper .Through the reaserching on the weakly damped Korteweg-de Vrie equations with initial condition and periodic boundary,we construct a semidiscrete Fourier spectral scheme for the equation and get a series of " energy equations" .Making full use of these "energy equations",we not only obtain a uniform priori estimate for the approximate solution of the semidiscrete Fourier spectral in time but also receive a good result.On these basis,we have further found the stability, the convergence and the error estimate of the semidiscrete Fourier spectral scheme over a finite time interval(0,T] under some conditions.And then,we discuss discrete dynamical systems which were generated by the semidiscrete Fourier spectral scheme .The existence of global attractor is proved for the dynamical system.