Perturbation-induced radiative losses in collision of NSE solitons

The total energy (and its spectral density) emitted during the collision of two solitons described by the conservatively perturbed non-linear Schrodinger equation (NSE) is calculated by means of perturbation theory based on the inverse scattering transform. It is shown that the total emitted energy (at large relative velocity) does not depend on the relative internal phase of the colliding solitons. The same results are obtained for solitons in a system of two weakly coupled non-linear Schrodinger equations.