Collision-induced amplitude dynamics of pulses in linear waveguides with the generic nonlinear loss

We study the effects of the generic weak nonlinear loss on fast two-pulse interactions in linear waveguides. The colliding pulses are described by a system of coupled Schr\"odinger equations with a purely nonlinear coupling in the presence of the weak $(2m+1)-$order of nonlinear loss, for any $m \geq 1$. We derive the analytic expression for the collision-induced amplitude shift in a fast two-pulse interaction. The analytic calculations are based on a generalization of the perturbation technique for calculating the effects of weak perturbations on fast collisions between solitons of the nonlinear Schr\"odinger equation. The theoretical predictions are confirmed by the numerical simulations with the full propagation model of coupled Schr\"odinger equations.