The degeneracy of Laplace invariants for hyperbolic systems possessing integrals

TL;DR

This paper extends the concept of Laplace invariants to hyperbolic PDE systems and proves that their determinant vanishes if the system admits an integral, linking invariants to integrability.

Contribution

It introduces a generalization of Laplace invariants for hyperbolic systems and establishes a criterion for integrals based on the invariants' degeneracy.

Findings

Determinant of Laplace invariant vanishes if the system admits an integral.

Provides a criterion linking invariants' degeneracy to integrability.

Generalizes classical Laplace invariants to hyperbolic PDE systems.

Abstract

A direct generalization of Laplace invariants to the case of hyperbolic partial differential systems is considered. The proof of the following statement is given: the determinant of a Laplace invariant vanishes if the corresponding system admits an integral.