Non-homogeneous systems of hydrodynamic type possessing Lax representations

TL;DR

This paper studies 1+1 dimensional non-homogeneous hydrodynamic systems with Lax representations, providing a construction method for many such systems and classifying the two-component case.

Contribution

It introduces a construction for a broad class of non-homogeneous hydrodynamic systems with Lax representations and classifies the two-component systems.

Findings

Provides a construction method for systems with Lax representations.

Classifies two-component systems within this class.

Expands understanding of integrable hydrodynamic systems.

Abstract

We consider 1+1 - dimensional non-homogeneous systems of hydrodynamic type that possess Lax representations with movable singularities. We present a construction, which provides a wide class of examples of such systems with arbitrary number of components. In the two-component case a classification is given.