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arXiv · 2109.11962

Kinetic equation for soliton gas: integrable reductions

E. V. Ferapontov·M. V. Pavlov
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Abstract

Macroscopic 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 2x2 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.

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E. V. Ferapontov, M. V. Pavlov. 2021-09-24. Kinetic equation for soliton gas: integrable reductions. https://doi.org/10.1007/s00332-022-09782-0

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