Generalized hydrodynamics of the KdV soliton gas

Thibault Bonnemain, Benjamin Doyon, Gennady El*

*Corresponding author for this work

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Abstract

We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg–de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons’ statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.
Original languageEnglish
Article number374004
Number of pages49
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number37
Early online date19 Aug 2022
DOIs
Publication statusPublished - 16 Sep 2022

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