On (2+1)-dimensional hydrodynamic type systems possessing pseudopotential with movable singularities

TL;DR

This paper classifies a class of integrable (2+1)-dimensional hydrodynamic systems with movable singularity pseudopotentials, providing explicit solutions and examples for arbitrary N.

Contribution

It introduces a functional equation characterizing integrable systems with movable singularity pseudopotentials and solves it explicitly, enabling construction of new integrable models.

Findings

Explicit solutions to the functional equation for integrable systems

Construction of examples of integrable hydrodynamic systems for any N

Identification of pseudopotential with movable singularities as a key integrability criterion

Abstract

A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable systems having pseudopotentials with movable singularities is described by a functional equation, which can be solved explicitly. This allows us to construct interesting examples of integrable hydrodynamic systems for arbitrary N.