Generalized Lie-B\"acklund theorem for Lie class \omega=1 overdetermined systems
Differential Geometry
2013-05-31 v2 Analysis of PDEs
Classical Analysis and ODEs
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.
Cite
@article{arxiv.1205.2914,
title = {Generalized Lie-B\"acklund theorem for Lie class \omega=1 overdetermined systems},
author = {Boris Kruglikov},
journal= {arXiv preprint arXiv:1205.2914},
year = {2013}
}
Comments
a typo is corrected: the truncated graded nilpotent Lie algebra n_k shall be n_{k+1}