Symmetry reduction of exterior differential systems and Bäcklund transformations for PDE in the plane

DOI10.1007/s10440-012-9716-0zbMath1287.37050arXiv1110.5777OpenAlexW2030017883MaRDI QIDQ384063

Ian M. Anderson, Mark E. Fels

Publication date: 25 November 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5777

zbMATH Keywords

Bäcklund transformationsexterior differential systemssymmetry reduction

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Invariance and symmetry properties for PDEs on manifolds (58J70) Exterior differential systems (Cartan theory) (58A15) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (7)

Bäcklund transformations and Darboux integrability, revisited ⋮ Rank 2 Bäcklund transformations of hyperbolic Monge-Ampère systems ⋮ Connections of zero curvature and applications to nonlinear partial differential equations ⋮ Geometry of Bäcklund transformations I: generality ⋮ Superposition formulas for exterior differential systems ⋮ Bäcklund transformations for Darboux integrable differential systems ⋮ Bäcklund transformations for Darboux integrable differential systems: examples and applications

Cites Work

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• Characteristics and the geometry of hyperbolic equations in the plane
• Integrating scalar ordinary differential equations with symmetry revisited
• Bäcklund transformations and Darboux integrability for nonlinear wave equations
• Superposition formulas for exterior differential systems
• Hyperbolic exterior differential systems and their conservation laws. I
• Characteristic cohomology of differential systems. II: Conservation laws for a class of parabolic equations
• Bäcklund transformations for Darboux integrable differential systems
• Exterior differential systems with symmetry
• Invariants of real low dimension Lie algebras

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