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

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journal contribution
posted on 26.02.2016 by F. Carbone, D. Dutykh, Gennady El
We undertake a detailed comparison of the results of direct numerical simulations of the soliton gas dynamics for the Korteweg-de Vries equation with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. 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) the collision of two cold soliton gases of different amplitudes (the soliton gas shock tube problem) leading to the formation of an expanding incoherent 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 the relevance of the kinetic equation for solitons as a quantitatively accurate model for macroscopic non-equilibrium dynamics of incoherent soliton ensembles.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Europhysics Letters: a letters journal exploring the frontiers of physics

Volume

113

Citation

CARBONE, F., DUTYKH, D. and EL, G.A., 2016. Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modelling. Europhysics Letters: a letters journal exploring the frontiers of physics, 113, 30003.

Publisher

© European Physical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016

Notes

This paper was accepted for publication in the journal Europhysics Letters and the definitive published version is available at http://dx.doi.org/10.1209/0295-5075/113/30003

ISSN

1286-4854

Language

en

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