Geometric theory of singularities of solutions of nonlinear differential equations

DOI10.1007/BF01095431zbMath1267.35056WikidataQ115394098 ScholiaQ115394098MaRDI QIDQ353069

Valentin V. Lychagin

Publication date: 12 July 2013

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear higher-order PDEs (35G20) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items

Meta-symplectic geometry of \(3^{\mathrm{rd}}\) order Monge-Ampère equations and their characteristics ⋮ Hamiltonian theory of constrained impulsive motion ⋮ From symmetries of partial differential equations towards secondary (``quantized) calculus ⋮ Singularities of Cauchy data, characteristics, cocharacteristics and integral cobordism ⋮ Characteristics, bicharacteristics and geometric singularities of solutions of PDEs ⋮ Under- and overdetermined systems of differential equations ⋮ Solution of a parabolic Hamilton-Jacobi type equation determined by a simple boundary singularity ⋮ Partial extensions of jets and the polar distribution on Grassmannians of non-maximal integral elements ⋮ Remarks on non-maximal integral elements of the Cartan plane in jet spaces ⋮ Rank two prolongations of second-order PDE and geometric singular solutions ⋮ On the plane into plane mappings of hydrodynamic type. Parabolic case ⋮ Singular Lagrangian manifolds and their Lagrangian maps

Cites Work

• Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
• Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena
• E. Cartan's geometrie theory of partial differential equations
• Existence theorems for analytic linear partial differential equations
• Integrability criteria for systems of nonlinear partial differential equations
• A Lefschetz fixed point formula for elliptic complexes. I
• The Hamilton-Cartan formalism in the calculus of variations
• Some Algebraic Results Concerning the Characteristics of Overdetermined Partial Differential Equations
• Overdetermined systems of linear partial differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item