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Generalized hydrodynamics of the KdV soliton gas

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Thibault Bonnemain, Benjamin Doyon, Gennady El

Original languageEnglish
Article number374004
JournalJournal of Physics A: Mathematical and Theoretical
Issue number37
Published16 Sep 2022

Bibliographical note

Funding Information: GE’s work was supported by EPSRC Grant EP/W032759/1. BD’s work was supported by EPSRC Grant EP/W010194/1. The authors thank G Roberti for sharing the numerical code for the nonlinear spectral synthesis of soliton gas. Publisher Copyright: © 2022 The Author(s). Published by IOP Publishing Ltd.

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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.

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