Dark-multi-soliton and soliton molecule solutions of stochastic nonlinear Schrödinger equation in the white noise space

Abstract

The wick-type nonlinear Schrödinger equation with gain and loss effects is studied. Dark-multi-soliton and dark soliton molecule solutions are obtained via the bilinear method and the Hermite transformation in the white noise space. The effects of gain and loss on the evolution of the dark-two-soliton molecule and the interaction between two dark solitons are analyzed. Moreover, the interaction between a dark-single-soliton and a dark-two-soliton molecule is discussed under the circumstance of the velocity resonance condition. The dark-three-soliton molecule is also considered. The results of this paper are useful for the study of soliton transmission in the white noise environment.