Direct perturbation method applied to three-dimensional nonlinear Schr?dinger equation

Abstract

By applying the direct perturbation method to the 3-dimensional nonlinear Schr&#246,dinger equation with perturbation, we obtain its asymptotical solutions, which contain not only the zero-order solutions, but also the first-order corrections. Through these solutions, the effect of perturbation on the soliton is analyzed as well.