Lie Theorem via Rank 2 Distributions (Integration of PDE of Class ω = 1)

DOI10.1142/S1402925112500118zbMath1255.35175arXiv1108.5854MaRDI QIDQ2905315

Boris S. Kruglikov

Publication date: 27 August 2012

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

Full work available at URL: https://arxiv.org/abs/1108.5854

zbMATH Keywords

distributionintegrabilityoverdetermined systempartial differential equationLaplace transformationreduction to ordinary differential equationLie class

Mathematics Subject Classification ID

Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72) Overdetermined problems for partial differential equations and systems of partial differential equations (35N99)

Related Items (7)

A solvable string on a Lorentzian surface ⋮ Veronese webs and nonlinear PDEs ⋮ Generalized Lie-Bäcklund theorem for Lie class overdetermined systems ⋮ Symmetry, compatibility and exact solutions of PDEs ⋮ Dispersionless integrable hierarchies and GL(2, ℝ) geometry ⋮ Null-forms of conic systems in \(\mathbb{R}^3\) are determined by their symmetries ⋮ On the models of submaximal symmetric rank 2 distributions in 5D

Cites Work

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• Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations
• Rank 2 distributions of Monge equations: symmetries, equivalences, extensions
• Geometric classes of Goursat flags and the arithmetics of their encoding by small growth vectors
• Superposition formulas for exterior differential systems
• On involutive systems of second order of codimension 2
• Flag systems and ordinary differential equations
• On differential systems, graded Lie algebras and pseudo-groups
• On local geometry of non-holonomic rank 2 distributions
• Geometry of differential equations
• Overdetermined systems of linear partial differential equations

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