Existence of Riemannian invariants for integrable systems of hydrodynamic type

TL;DR

This paper demonstrates that hyperbolic hydrodynamic systems with symmetries can be transformed into a coordinate system where the system and its symmetries are diagonal, revealing underlying Riemannian invariants.

Contribution

It establishes the existence of Riemannian invariants for integrable hydrodynamic systems and shows their diagonalization in suitable coordinates.

Findings

Existence of coordinate systems diagonalizing the system and symmetries.

Identification of Riemannian invariants in integrable hydrodynamic systems.

Applicability to systems with multiple symmetries.

Abstract

We show that for a hyperbolic system of hydrodynamic type admitting n symmetries, there exists a coordinate system in which the generator of the system and all the symmetries are diagonal.