Symmetry Approaches for Reductions of PDEs, Differential Constraints and Lagrange-Charpit Method
Copyright policy )Symmetry Approaches for Reductions of PDEs, Differential Constraints and Lagrange-Charpit Method
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.
Mathematics - Differential Geometry, 34A05, 35N10, 58A20, 35A30, Overdetermined systems of PDEs with variable coefficients, reduction, VDP::Mathematics and natural science: 400::Mathematics: 410::Topology/geometry: 415, compatibility, Compatibility, homological methods, Invariance and symmetry properties for PDEs on manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), 34A05, 35N10; 58A20, 35A30, FOS: Mathematics, multi-bracket, differential constraint, Jets in global analysis, solvability, symmetry, Geometric theory, characteristics, transformations in context of PDEs, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, 34A05, 35N10, 58A20, 35A30, Overdetermined systems of PDEs with variable coefficients, reduction, VDP::Mathematics and natural science: 400::Mathematics: 410::Topology/geometry: 415, compatibility, Compatibility, homological methods, Invariance and symmetry properties for PDEs on manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), 34A05, 35N10; 58A20, 35A30, FOS: Mathematics, multi-bracket, differential constraint, Jets in global analysis, solvability, symmetry, Geometric theory, characteristics, transformations in context of PDEs, Analysis of PDEs (math.AP)
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