Holonomic systems of Clairaut type

DOI10.1016/0926-2245(95)92847-XzbMath0832.35028OpenAlexW2005905318WikidataQ115362541 ScholiaQ115362541MaRDI QIDQ1900153

Yasuhiro Kurokawa, Shyuichi Izumiya

Publication date: 17 October 1995

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0926-2245(95)92847-x

zbMATH Keywords

Clairaut equationcomplete solutions

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items (8)

Spacelike parallels and evolutes in Minkowski pseudo-spheres ⋮ On implicit second-order ordinary differential equations: Completely integrable and Clairaut type ⋮ Bifurcations of completely integrable 2-variable first-order partial differential equations ⋮ The theory of graph-like Legendrian unfoldings and its applications ⋮ Bifurcations of ordinary differential equations of Clairaut type ⋮ Singularities of singular solutions of first-order differential equations of clairaut type ⋮ Generic singularities of implicit systems of first order differential equations on the plane ⋮ On families of Lagrangian submanifolds

Cites Work

• Reconstructions of fronts and caustics depending on a parameter and versality of mappings
• Familles de courbes planes différentiables
• Modules pour les familles de courbes planes. (Moduli for the families of plane curves)
• Singularities of envelopes of families of submanifolds in $\mathbb{R}^N$
• The unfolding and determinacy theorems for subgroups of 𝒜 and 𝒦
• LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
• The theory of Legendrian unfoldings and first-order differential equations
• Determinacy of the Envelope of the Osculating Hyperplanes to a Curve
• Systems of Clairaut type
• Completely integrable holonomic systems of first-order differential equations
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