Stochastic Ginzburg-Landau equation is numerically studied.A nonlinear difference scheme and a linearized scheme which avoid iteration in implementation are constructed.Numerical solutions of both deterministic equation and stochastic equation show accuracy and efficiency of the difference schemes.Numerical experiments with different noise amplitudes are presented and different types of behaviors are described.

A pertured sine-Gordon equation u_tt-u_xx+αsinu-βu_xxt=g(u),t>0,-∞< x< ∞,with the periodic initial and boundary value problem is studied. A spectral method is proposed,a priori estimates are established and the existnce and uniqueness are proved for the generalized solution.The error estimates are given and the convergence is proved for the approximate solution of the spectral method.

In this paper, We consider solitary waves induced by boundary pulses for regularized Long-wave equation. A conservative difference scheme is presented for the equation. Using the scheme, solitary waves induced by several boundary pulses are computed numerically. We explore the relationship between the amplitudes and numbers of the solitons produced and the boundary pulses, and compare solitons induced by the boundary pulse with ones produced ny initial pulses.