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Title: Kinetic equation for a soliton gas and its hydrodynamic reductions
Authors: El, G.A.
Kamchatnov, A.M.
Pavlov, Maxim V.
Zykov, S.A.
Keywords: Soliton gas
Thermodynamic limit
Kinetic equation
Hydrodynamic reduction
Integrability
Issue Date: 2011
Publisher: © Springer
Citation: EL, G.A. ... et al., 2011. Kinetic equation for a soliton gas and its hydrodynamic reductions. Journal of Nonlinear Science, 21 (2), pp. 151-191.
Abstract: We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N-component 'cold-gas' hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the 'cold-gas' component densities and construct a number of exact solutions having special properties (quasi-periodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed the light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s00332-010-9080-z.
Sponsor: The work has been partially supported by EPSRC (UK)(grant EP/E040160/1) and London Mathematical Society (Scheme 4 Collaborative Visits Grant). Work of M.V.P. has been also supported by the Programme "Fundamental problems of nonlinear dynamics" of Presidium of RAS. M.V.P. and S.A.Z. also acknowledge partial financial support from the Russian-Taiwanese grant 95WFE0300007 (RFBR grant 06-01-89507-HHC).
Version: Accepted for publication
DOI: 10.1007/s00332-010-9080-z
URI: https://dspace.lboro.ac.uk/2134/15335
Publisher Link: http://dx.doi.org/10.1007/s00332-010-9080-z
ISSN: 0938-8974
Appears in Collections:Published Articles (Maths)

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