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

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