English

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.

Keywords

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}

R2 v1 2026-06-21T21:03:10.783Z