Generalised hydrodynamic reductions of the kinetic equation for soliton gas

TL;DR

This paper develops generalized hydrodynamic reductions for the kinetic equation describing soliton gases, revealing new integrable systems that extend traditional frameworks and deepen understanding of soliton gas dynamics.

Contribution

It introduces a novel class of integrable hydrodynamic systems derived from the kinetic equation for soliton gases, expanding the theoretical landscape.

Findings

New multi-flow hydrodynamic reductions derived

Insights into properties of the kinetic equation for soliton gases

Potential identification of a new class of integrable systems

Abstract

We derive generalised multi-flow hydrodynamic reductions of the nonlocal kinetic equation for a soliton gas and investigate their structure. These reductions not only provide further insight into the properties of the new kinetic equation but also could prove to be representatives of a novel class of integrable systems of hydrodynamic type, beyond the conventional semi-Hamiltonian framework.