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

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.

20 pages, 8 figures, 34 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (2)

• Soliton Turbulence in Shallow Water Ocean Surface Waves
• Critical density of a soliton gas

Cited by in corpus (24)

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• Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves
• Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
• Transport fluctuations in integrable models out of equilibrium
• Generalized Gibbs Ensembles of the classical Toda chain
• Ballistic macroscopic fluctuation theory
• Rigorous asymptotics of a KdV soliton gas
• Form factors and generalized hydrodynamics for integrable systems
• Soliton gas in bidirectional dispersive hydrodynamics
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• The GGE averaged currents of the classical Toda chain
• Experimental study of integrable turbulence in shallow water
• Analysis of soliton gas with large-scale video-based wave measurements
• Free energy fluxes and the Kubo-Martin-Schwinger relation
• Soliton spectra of random water waves in shallow basins
• On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties
• $T\overline{T}$ deformations and the width of fundamental particles
• Travelling wave solutions on a non-zero background for the generalized Korteweg-de Vries equation
• Dynamics of Interaction of Two Soliton Clouds
• The formation of a soliton gas condensate for the focusing Nonlinear Schrödinger equation