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

## TL;DR

This paper shows that pulses in weakly nonlinear-perturbed linear systems behave like solitons during fast collisions, with similar amplitude shift expressions as optical solitons, confirmed by numerical simulations.

## Contribution

It demonstrates soliton-like behavior in linear systems with weak nonlinear dissipation during fast collisions, extending soliton concepts beyond nonlinear integrable systems.

## Key findings

- Collision-induced amplitude shifts match those in optical solitons.
- Analytic predictions align with numerical simulations.
- Results apply to various linear systems with weak nonlinear loss.

## Abstract

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 optical solitons 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.