Approximate Solutions of Perturbed Nonlinear Schr(?)dinger Equations

<正> By applying Lou's direct perturbation method to perturbed nonlinear Schrdinger equation and the criticalnonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-orderand the first-order solutions are obtained.Based on these approximate solutions,the analytical forms of parameters ofsolitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time.In addition,theperturbed nonlinear Schrdinger equations is directly simulated by split-step Fourier method to check the validity of thedirect perturbation method.It turns out that the analytical results given by the direct perturbation method are wellsupported by numerical calculations.