Laplace transformation of Lie class \omega=1 overdetermined systems

TL;DR

This paper explores the use of Laplace transformation to linearize and integrate overdetermined scalar PDE systems with a common characteristic, connecting classical Lie theory with modern PDE formalism.

Contribution

It introduces a method for linearizing and solving specific overdetermined PDE systems using Laplace transformation, linking it to Lie's integration theorem.

Findings

Laplace transformation effectively linearizes certain PDE systems.

The approach relates classical Lie theory to modern PDE integration methods.

Provides a framework for solving PDEs with a common characteristic.

Abstract

In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs.