On the local stability of wave fronts defined by eikonal equations

DOI10.1017/S0308210500011811zbMath0429.58017OpenAlexW2322893554MaRDI QIDQ3866820

David A. Rand

Publication date: 1980

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500011811

zbMATH Keywords

contact structurealgebraic characterization of local solutions of eikonal equations which have stable wave front structuresfirst order scalar partial differential equationLegendrian submanifold of the 1-jet bundleThom's elementary catastrophes

Mathematics Subject Classification ID

Partial differential equations on manifolds; differential operators (58J99) Catastrophe theory (58K35) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Hyperbolic equations on manifolds (58J45)

Related Items (1)

Applications of catastrophe theory to the physical sciences

Cites Work

• Caustics and catastrophes
• Catastrophes and partial differential equations
• Caustics and non-degenerate Hamiltonians
• Stability of unfoldings in space and time
• Lagrangian and Legendrian singularities
• Fourier integral operators. I
• LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
• CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS
• Wave front evolution and equivariant Morse lemma
• Oscillatory integrals, lagrange immersions and unfolding of singularities

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