Universality of the amplitude shift in fast two-pulse collisions in weakly perturbed linear physical systems

We demonstrate that the amplitude shifts in fast two-pulse collisions perturbed linear physical systems with weak nonlinear dissipation exhibit universal soliton-like behavior. The behavior is demonstrated for optical waveguides cubic loss and described by diffusion-advection models quadratic loss. show both systems, expressions collision-induced due to have same form as expression obtained a collision between two solitons of Schr\"odinger equation presence Furthermore, we are sense they independent exact details initial pulse shapes. carrying out numerical simulations coupled evolution three different conditions corresponding pulses exponentially decreasing tails, power-law initially nonsmooth develop significant tails during collision. In all six cases observe very good agreement analytic predictions results simulations.