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

2013/08/01 by S. Yu. Dobrokhotov, G. Makrakis, V. E. Nazaikinskii +1
Mathematics · Physics and Astronomy · #math-ph #math.AP #math.MP #msc:35S30 #msc:81Q20

paper · pdf · doi:10.1007/s11232-013-0123-0

26 pages. Submitted to "Theoretical and Mathematical Physics"

arxiv created 2013/08/01 · arxiv updated 2015/06/16

Abstract

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].

Citations

• Fourier integrals and a new representation of Maslov's canonical operator near caustics