On the amplitude dynamics of solitons in waveguide systems with the generic Kerr nonlinearity coefficient and nonlinear gain-loss

Abstract

We study the transmission of optical solitons in a nonlinear waveguide with the generic Kerr nonlinearity coefficient, the frequency dependent linear gain-loss, and the Ginzburg-Landau (GL) gain-loss profile. We first derive the expression for the collision-induced amplitude dynamics of two fast single solitons in the presence of weak cubic loss and weak quintic loss. This expression is then used to study the amplitude dynamics of solitons in multichannel optical waveguide systems. We show that the dynamics of soliton amplitudes in two-sequence transmission with the GL gain-loss profile are described by a Lotka-Volterra (LV) model. The stability analysis for the LV model is used to obtain the simple conditions on the physical parameters and to calculate the linear amplifier gain-loss for the transmission stabilization of the soliton sequences. The theoretical calculations are then confirmed by numerical simulations with the corresponding nonlinear Schrödinger (NLS) models. Furthermore, the optimal value of the Kerr nonlinearity coefficient for the robust transmission stabilization of the soliton sequences with the GL gain-loss profile is also proposed.