Metamorphism -- an Integral Transform Reducing the Order of a Differential Equation

TL;DR

This paper introduces 'metamorphism,' an integral transform that reduces the order of differential equations, exemplified by transforming the Helmholtz equation into a first order form solvable by characteristics.

Contribution

The paper presents a novel integral transform called metamorphism that simplifies differential equations by reducing their order, facilitating easier solutions.

Findings

Helmholtz equation reduced from second to first order

Metamorphism enables solving reduced equations via characteristics

Transform applicable to various differential equations

Abstract

We propose an integral transform, called metamorphism, which allow us to reduce the order of a differential equation. For example, the second order Helmholtz equation is transformed into a first order equation, which can be solved by the method of characteristics.