Interaction of the nonautonomous soliton in the optical fiber

Investigated in this paper is a generalized nonautonomous nonlinear Schrödinger equation with both external potential and phase modulation, which can be used to described the nonautonomous soliton in the optical fiber. With our results as follows: Lax pair, Daboux transformation, condition of the modulation instability and N−soliton solutions have been obtained; Propagation and interaction of the solitons have been analysed: (1) the group velocity and linear potential affect the direction and trajectory of one/two solitons′ propagation, respectively; (2) two solitons have the same average velocity at some fixed time or a period.