Ferapontov-Pavlov2022_Article_KineticEquationForSolitonGasIn.pdf (452.27 kB)
Kinetic equation for soliton gas: integrable reductions
journal contribution
posted on 2022-03-11, 14:36 authored by Evgeny FerapontovEvgeny Ferapontov, M.V. PavlovMacroscopic dynamics of soliton gases can be analytically described by the thermodynamic limit of the Whitham equations, yielding an integro-differential kinetic equation for the density of states. Under a delta-functional ansatz, the kinetic equation for soliton gas reduces to a non-diagonalisable system of hydrodynamic type whose matrix consists of several 2 × 2 Jordan blocks. Here we demonstrate the integrability of this system by showing that it possesses a hierarchy of commuting hydrodynamic flows and can be solved by an extension of the generalised hodograph method. Our approach is a generalisation of Tsarev’s theory of diagonalisable systems of hydrodynamic type to quasilinear systems with non-trivial Jordan block structure.
Funding
Russian Science Foundation No. 21-11-00006, https://rscf.ru/project/21-11-00006/
Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2021-1748)
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Nonlinear ScienceVolume
32Issue
2Publisher
SpringerVersion
- VoR (Version of Record)
Rights holder
© The AuthorsPublisher statement
This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/Acceptance date
2022-02-04Publication date
2022-03-04Copyright date
2022ISSN
0938-8974eISSN
1432-1467Publisher version
Language
- en
Depositor
Prof Evgeny Ferapontov. Deposit date: 6 February 2022Article number
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