Classification of integrable hydrodynamic chains

TL;DR

This paper classifies integrable hydrodynamic chains in (1+1) and (2+1) dimensions using hydrodynamic reductions, providing a comprehensive understanding of their integrability conditions.

Contribution

It systematically identifies all integrable infinite hydrodynamic chains of shift one in (1+1) dimensions and constructs a class in (2+1) dimensions.

Findings

Complete classification of (1+1)-dimensional integrable chains.

Construction of a new class of (2+1)-dimensional integrable chains.

Application of hydrodynamic reduction method to establish integrability.

Abstract

Using the method of hydrodynamic reductions, we find all integrable infinite (1+1)-dimensional hydrodynamic-type chains of shift one. A class of integrable infinite (2+1)-dimensional hydrodynamic-type chains is constructed.