A reduction procedure for determining exact solutions of second order hyperbolic equations

TL;DR

This paper introduces a systematic reduction method for second order hyperbolic equations, enabling the derivation of exact solutions through first order PDEs, with specific conditions and classifications provided.

Contribution

It presents a novel reduction procedure for solving second order hyperbolic PDEs by linking them to first order PDEs, including characterizations of linear cases.

Findings

Reduction procedure for second order hyperbolic equations

Conditions for the applicability of the method

Characterization of linear hyperbolic equations

Abstract

In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order PDEs. We give some conditions in order that such a procedure holds and, in particular, we characterize classes of linear second order hyperbolic equations for which the general solution can be found.