Radiation dynamics in fast soliton collisions in the presence of cubic loss

Abstract

We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schr\"odinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a perturbation technique with two small parameters: the cubic loss coefficient $\epsilon_{3}$ and the reciprocal of the group velocity difference $1/\beta$. The agreement between the perturbation theory predictions and the results of numerical simulations with the full coupled-NLS propagation model is very good for large $\beta$ values, and is good for intermediate $\beta$ values. Additional numerical simulations with four simplified NLS models show that the differences between perturbation theory and simulations for intermediate $\beta$ values are due to the effects of Kerr nonlinearity on interpulse interaction in the collision. Thus, our study demonstrates that the perturbation technique that was originally developed to study radiation dynamics in fast soliton collisions in the presence of conservative perturbations can also be employed for soliton collisions in the presence of dissipative perturbations.