Generalized Lie-Bäcklund theorem for Lie class ω=1 overdetermined systems

Abstract

In this paper we prove a version of Lie-Bäcklund 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.

arXiv commenta typo is corrected: the truncated graded nilpotent Lie algebra n_k shall be n_{k+1}