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arxiv: 1308.0182 · v1 · pith:QTBIRIMOnew · submitted 2013-08-01 · 🧮 math-ph · math.AP· math.MP

New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics

S. Yu. Dobrokhotov (1 , 2) , G. Makrakis (3 , 4) , V. E. Nazaikinskii (1 , T. Ya. Tudorovskii (5) ((1) A. Ishlinsky Institute for Problems in Mechanics , Moscow , Russia
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(2) Moscow Institute of Physics Technology Dolgoprudny Moscow District (3) Department of Applied Mathematics University of Crete Heraklion Crete Greece (4) Institute of Applied Computational Mathematics Foundation for Research Technology-Hellas (5) Radboud University Nijmegen Institute for Molecules Materials the Netherlands)
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classification 🧮 math-ph math.APmath.MP
keywords canonicalcasecausticsmaslovneighborhoodoperatorarxivasymptotics
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We suggest a new representation of Maslov's canonical operator in a neighborhood of the caustics using a special class of coordinate systems ("eikonal coordinates") on Lagrangian manifolds. The specific features of the two-dimensional case are considered. The general case is treated in arXiv:1307.2292 [math-ph].

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