Reducibility of Euler integrals and multiintegrals

TL;DR

This paper explores the reduction of Euler integrals and multiintegrals, providing algorithms and proving the equivalence of different reduction definitions, advancing the understanding of integrable systems and solution methods.

Contribution

It introduces algorithms for reducing Euler integrals and multiintegrals, establishing the equivalence of various reduction definitions in the context of integrable systems.

Findings

Algorithms for reduction of Euler integrals and multiintegrals are developed.

Different natural definitions of reduction are proven to be equivalent.

The work extends classical solution methods for hyperbolic equations.

Abstract

We discuss the notion of reduction of a special type of explicit solutions which generalize the solutions appearing in the classical Laplace cascade method of integration of hyperbolic equations of the second order in the plane. We give algorithms of reduction and prove that different natural precise definitions of reduction are equivalent. Keywords: cascade integration method, integrable systems, Euler integrals.