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

Francesco Carbone (1) , Denys Dutykh (2) , Gennady El (3)

1 CNR-IIA - Istituto Inquinamento Atmosferico (C.N.R.)
2 LAMA - Laboratoire de Mathématiques
3 Department of Mathematical Sciences, Loughborough University

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.

Mots clés: soliton gas; Korteweg-de Vries equation; integrable turbulence; kinetic equation; direct numerical simulations

Domaines: Mécanique des fluides [physics.class-ph]; Formation de Structures et Solitons [nlin.PS]; Systèmes Solubles et Intégrables [nlin.SI]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]

Francesco Carbone, Denys Dutykh, Gennady El. Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling: Incoherent soliton ensembles. 2015. ⟨hal-01248680v1⟩