Symmetry, compatibility and exact solutions of PDEs

2011/11/24 by Boris Kruglikov, Kruglikov, Boris
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1111.5856

Two more examples are added to section 2

openalex publication_date 2011/11/24 · arxiv created 2012/03/04 · arxiv updated 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra of symmetries has invariant solutions with respect to this Lie algebra. These conditions hold for generic=nondegenerate pairs (equation,symmetry) in certain dimension range for the Lie algebra. Finally we discuss models of equations with large symmetry algebras, which eventually lead to integration in closed form.

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