Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations |
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| Authors: | S Yu Dobrokhotov B Tirozzi C A Vargas |
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| Institution: | (1) A. Ishlinski Institute for Problems in Mechanics, RAS, Moscow, Russia;(2) Moscow Institute of Physics and Technology, Moscow, Russia;(3) Department of Physics, University “La Sapienza”, Rome, Italy;(4) Institute of Applied Mathematics and Systems, FENOMEC, Universidad Nacional Autonoma de Mexico (UNAM), San Antonio, Mexico |
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| Abstract: | We study the behavior of the wave part of asymptotic solutions to the Cauchy problem for linearized shallow water equations
with initial perturbations localized near the origin. The global representation for these solutions based on the generalized
Maslov canonical operator was given earlier. The asymptotic solutions are also localized in the neighborhood of certain curves
(fronts). The simplification of general formulas and the behavior of asymptotic solutions in a neighborhood of the regular
part of fronts was also given earlier. Here the behavior of asymptotic solutions in a neighborhood of the focal point of the
fronts is discussed in detail and the proof of formulas announced earlier for the wave equation is given. This paper can be
regarded as a continuation of the paper in Russiian Journal of Mathematical Physics 15 (2), 192–221 (2008).
In memoriam V.A. Borovikov |
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