Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method

2007/12/20 by Boris Kruglikov, Kruglikov, Boris
Mathematics · Physics and Astronomy · #34A05 #35A30 #35N10 #58A20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum chaos and dynamical systems #math.AP #math.DG #msc:34A05 #msc:35A30 #msc:35N10 #msc:58A20

paper · pdf · doi:10.48550/arxiv.0712.3425

arxiv created 2007/12/20 · openalex publication_date 2007/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many methods for reducing and simplifying differential equations are known. They provide various generalizations of the original symmetry approach of Sophus Lie. Plenty of relations between them have been noticed and in this note a unifying approach will be discussed. It is rather close to the classical differential constraint method, but we provide certain rigorous results basing on recent advances in compatibility theory of non-linear overdetermined systems and homological methods for PDEs.

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