Generalized hydrodynamics of the KdV soliton gas

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.

arXiv comment48 pages, 7 figures

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Cited by in corpus (5)

• Ballistic macroscopic fluctuation theory
• Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
• Soliton shielding of the focusing Nonlinear Schrödinger Equation
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• Properties of synchronous collisions of solitons in the Korteweg - de Vries equation