A new approach to exact soliton solutions and soliton interaction for the nonlinear Schrödinger equation with variable coefficients

Abstract

In this paper, the generalized nonlinear Schrödinger equation with variable coefficients is considered from the integrable point of view, and an exact multi-soliton solution is presented by employing the simple, straightforward Darboux transformation based on the Lax Pair, and then one- and two-soliton solutions in explicit forms are generated. As an example, we consider the distributed amplification system, and some main features of solutions are shown. The results reveal that the combined effects of controlling both the group velocity dispersion distribution and the nonlinearity distribution can restrict the interaction between the neighboring solitons. Also, by simulating numerically, the stability of the neighboring solitons with respect to the finite perturbations is discussed in detail. Finally, under nonintegrable condition the evolution of soliton is in detail discussed.