Soliton splitting in quenched classical integrable systems

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 $η$ and take the obtained profile as a new initial condition. We find the values of $η$ 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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