A geometric interpretation of prolongation by means of connections

DOI10.1063/1.3504172zbMath1314.35012OpenAlexW1964003079MaRDI QIDQ5254858

Paul Bracken

Publication date: 10 June 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3504172

Mathematics Subject Classification ID

Continuation and prolongation of solutions to PDEs (35B60) Linear and affine connections (53B05) Fiber bundles in algebraic topology (55R10) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (5)

Exterior differential expression of the \((1+1)\)-dimensional nonlinear evolution equation with Lax integrability ⋮ Connections of zero curvature and applications to nonlinear partial differential equations ⋮ The prolongation structure of a coupled KdV equation ⋮ GEOMETRIC APPROACHES TO PRODUCE PROLONGATIONS FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ⋮ A geometric formulation of Lax integrability for nonlinear equations in two independent variables

Cites Work

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• An exterior differential system for a generalized Korteweg-de Vries equation and its associated integrability
• Bäcklund transformations, the inverse scattering method, solitons, and their applications. NSF research workshop on contact transformations
• An analogue of Bäcklund's theorem in affine geometry
• The KdV prolongation algebra
• Moving frames and prolongation algebras
• Prolongation structures of nonlinear evolution equations
• Prolongation structures of nonlinear evolution equations. II

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