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

2012/05/13 by Boris Kruglikov, Kruglikov, Boris
Mathematics · Physics and Astronomy · #58J70 #58J72 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.AP #math.CA #math.DG #msc:58J70 #msc:58J72

paper · pdf · doi:10.48550/arxiv.1205.2914

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

openalex publication_date 2012/05/13 · arxiv created 2013/05/30 · arxiv updated 2013/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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