Soliton splitting in quenched classical integrable systems

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 Schrödinger integrable equations.

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Cited by in corpus (6)

• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Excitation modes of bright matter-wave solitons
• Integrable Matrix Models in Discrete Space-Time
• Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases
• Interplay of Solitons and Radiation in One-Dimensional Bose Gases
• Non-reciprocal breathing solitons