Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term

An exchange in the wave action (number of quanta) is analyzed by means of the perturbation theory for a soliton-soliton collision in the nonlinear Schrödinger equation with a nonlinear damping term that conserves the total wave action (it may account for the intrapulse Raman scattering in the model of a lossless optical fiber, or for the nonlinear Landau damping in a plasma). It is demonstrated that, if the colliding solitons have a sufficiently large relative velocity, the analytical results are in very good accordance with recently published numerical simulations [S. Chi and S. Wen, Opt. Lett. 14, 1216 (1989)]. This warrants application of the present variant of the perturbative technique to other physical problems.