Construction of uniform asymptotic solutions of wave-type differential equations by methods of catastrophe theory

DOI10.1134/S1061920809020083zbMath1180.35503MaRDI QIDQ1033842

A. S. Kryukovskii, D. S. Lukin, D. V. Rastyagaev

Publication date: 10 November 2009

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

zbMATH Keywords

singularitiesasymptotic solutionswave catastrophe theory

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Diffraction, scattering (78A45) Asymptotic expansions of solutions to PDEs (35C20) Theoretical approximation in context of PDEs (35A35) Singularities of differentiable mappings in differential topology (57R45) Differentiable maps on manifolds (58C25)

Related Items (2)

Local asymptotics of unfoldings of edge and corner catastrophes ⋮ Contour integral solutions of the parabolic wave equation

Cites Work

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• Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
• Classification of unimodal and bimodal corner singularities
• Corner catastrophes and uniform asymptotics
• SINGULARITIES OF FUNCTIONS ON BOUNDARIES, CORNERS, ETC.
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• Uniform asymptotic expansions at a caustic
• Uniform Asymptotic Expansions for Saddle Point Integrals-Application to a Probability Distribution Occurring in Noise Theory

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