On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems

TL;DR

This paper investigates a special class of integrable two-component (2+1)-dimensional hydrodynamic systems, extending Hamiltonian cases, and provides a parametric integration and dispersionless Lax formulation.

Contribution

It introduces a new integrability analysis for a specific class of hydrodynamic systems, generalizing known Hamiltonian cases with explicit parametric solutions.

Findings

System in involution is integrated parametrically

A dispersionless Lax formulation is established

Extends integrability to a broader class of systems

Abstract

The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A dispersionless Lax formulation is found.