Soliton splitting in quenched classical integrable systems

TL;DR

This paper investigates how solitons in classical integrable systems respond to sudden parameter changes, revealing conditions for the emergence of a finite number of solitons post-quench through analytical scattering methods.

Contribution

It introduces an analytical approach to determine soliton outcomes after a parameter quench in several classical integrable equations, providing explicit soliton parameters.

Findings

Identifies specific quench parameters leading to finite soliton solutions

Provides explicit formulas for post-quench soliton parameters

Demonstrates method on Korteweg-de Vries, sine-Gordon, and nonlinear Schrödinger equations

Abstract

We take a soliton solution of a classical non-linear integrable equation and quench (suddenly change) its non-linearity parameter. For that we multiply the amplitude or the width of a soliton by a numerical factor $\eta$ and take the obtained profile as a new initial condition. We find the values of $\eta$ at which the post-quench solution consists of only a finite number of solitons. The parameters of these solitons are found explicitly. Our approach is based on solving the direct scattering problem analytically. We demonstrate how it works for Kortewig-de-Vries, sine-Gordon and non-linear Schr\"odinger integrable equations.