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

Abstract

We demonstrate the universal soliton-like behavior of the amplitude shifts in fast two-pulse collisions in perturbed linear physical systems with weak nonlinear dissipation. The behavior is demonstrated for linear optical waveguides with weak cubic loss and for systems described by linear diffusion–advection models with weak quadratic loss. We show by a perturbative calculation that in both systems, the expressions for the collision-induced amplitude shifts due to nonlinear loss have the same form as the expression obtained for a fast collision between solitons of the nonlinear Schrödinger equation in the presence of weak cubic loss. Moreover, we show that the expressions for the amplitude shifts are universal in the sense that they are independent of the details of the initial pulse shapes. We check the analytic predictions by extensive numerical simulations with the two perturbed linear evolution models with four major types of initial pulses corresponding to pulses with exponentially decreasing tails, two types of pulses with power-law decreasing tails, and pulses that are initially nonsmooth. In all cases, we observe a very good agreement between analytic predictions and numerical simulations. Thus, our study significantly generalizes the results of previous studies, which were limited to the special case of Gaussian-pulse collisions.