Generalized hydrodynamics of the KdV soliton gas

TL;DR

This paper establishes a connection between soliton gas theory in classical integrable systems and generalized hydrodynamics, providing explicit formulas and numerical validation for the KdV equation's soliton gas.

Contribution

It constructs the GHD description for the KdV soliton gas, predicts exact thermodynamic quantities, and confirms static correlations through numerical simulations.

Findings

Derived explicit GHD description for KdV soliton gas

Predicted exact free energy density and flux for the gas

Validated static correlation matrices with numerical simulations

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 (KdV) 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.