Generalized Lie-B\"acklund theorem for Lie class \omega=1 overdetermined systems

TL;DR

This paper extends the Lie-Bäcklund theorem to certain overdetermined PDE systems with solutions depending on one function of one variable, generalizing classical results and providing numerous examples.

Contribution

It introduces a generalized Lie-Bäcklund theorem for overdetermined scalar PDE systems with Lie class =1, expanding the classical involutive case.

Findings

Proves a generalized Lie-Bäcklund theorem for =1 systems

Provides multiple illustrative examples

Extends classical involutive system results

Abstract

In this paper we prove a version of Lie-B\"acklund theorem for overdetermined systems of scalar PDEs, whose general solution depends on 1 function of 1 variable. This generalizes the case of involutive system of the second order on the plane treated by E.Cartan in 1910. Many examples are provided.