# Nonlocal Hydrodynamic Type of Equations

## TL;DR

This paper demonstrates that integrable hydrodynamic equations can be reduced to nonlocal forms, which remain integrable and possess Lax representations, expanding the understanding of their structure and conservation laws.

## Contribution

It introduces a method to construct nonlocal reductions of integrable hydrodynamic equations and provides explicit examples demonstrating their integrability and conserved quantities.

## Key findings

- Nonlocal reductions of hydrodynamic equations are integrable.
- Reduced equations admit Lax representations.
- They possess infinitely many conserved quantities.

## Abstract

We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of hydrodynamic type and integrable. They admit Lax representations and hence possess infinitely many conserved quantities.