Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems

We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems described by linear diffusion–advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression for the amplitude shift in a fast collision between two solitons of the cubic nonlinear Schrödinger equation in the presence of weak cubic loss. Our analytic predictions are confirmed by numerical simulations with the corresponding coupled linear evolution models with weak nonlinear loss. These results open the way for studying dynamics of fast collisions between pulses of weakly perturbed linear physical systems in an arbitrary spatial dimension. Graphical abstract