How to kick a soliton ?

TL;DR

This paper introduces a perturbative method to analyze how solitons in dissipative systems respond to impulsive external forces, validated through numerical simulations of kinks and skyrmions.

Contribution

A novel perturbative scheme that accurately captures nonlinear soliton responses in dissipative systems, applicable to models with second order derivatives.

Findings

Method successfully applied to 1+1D kinks and 2+1D skyrmions

Captures genuine nonlinear phenomena in soliton dynamics

Extension to second order time derivative models discussed

Abstract

A simple method how to study response of solitons in dissipative systems to external impulsive perturbations is developed. Thanks to nontrivial choice of small parameter, the perturbative scheme captures genuine nonlinear phenomena. The method is developed and tested by numerical simulations for kinks in 1+1 dimensions and for skyrmions in 2+1 dimensions. Extension to models including second order time derivatives is discussed.