Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling

TL;DR

This paper compares numerical simulations with analytical kinetic equations for soliton gases in the KdV model, confirming the equations' accuracy in describing macroscopic dynamics of incoherent soliton ensembles.

Contribution

It provides the first detailed validation of soliton gas kinetic equations against direct numerical simulations in the KdV system.

Findings

Excellent agreement between simulations and analytical predictions.

Kinetic equation accurately models non-equilibrium soliton gas dynamics.

Results support the use of kinetic theory for integrable soliton systems.

Abstract

We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use the KdV soliton gas as a simplest analytically accessible model yielding major insight into the general properties of soliton gases in integrable systems. Two model problems are considered: (i) the propagation of a `trial' soliton through a one-component `cold' soliton gas consisting of randomly distributed solitons of approximately the same amplitude; and (ii) collision of two cold soliton gases of different amplitudes (soliton gas shock tube problem) leading to the formation of an incoherend dispersive shock wave. In both cases excellent agreement is observed between the analytical predictions of the soliton gas kinetics and the direct numerical simulations. Our results confirm relevance of the kinetic equation for solitons as a quantitatively accurate model for macroscopic non-equilibrium dynamics of incoherent soliton ensembles.