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This article is cited in 1 scientific paper (total in 1 paper)
Asymptotics of the Helmholtz equation solutions in a two-layer medium with a localized right-hand side
A. Yu. Anikin, A. I. Klevin Ishlinsky Institute for Problems in Mechanics, Russian
Academy of Sciences, Moscow, Russia
Abstract:
We construct the leading term of the semiclassical asymptotic solution of the Helmholtz equation with a small parameter in the localized right-hand side. This equation arises, for example, in the problem of ocean acoustics, in which the small parameter is given by the ratio of the characteristic scale of the “vertical” coordinate to that of the other coordinates. The equation is considered in the region bounded in the “vertical” coordinate; it is divided into two layers, with the coefficient in the Helmholtz equation and the derivative of the solution having fixed jump discontinuities at the interface. The technique for constructing the asymptotics involves the operator separation of variables (adiabatic approximation) and the use of the recently developed method for constructing asymptotics of equations with localized right-hand sides in the equations obtained after the variable separation.
Keywords:
Helmholtz equation, equation with a right-hand side, semiclassical
asymptotics, Maslov canonical operator.
Received: 13.12.2022 Revised: 15.02.2023
Citation:
A. Yu. Anikin, A. I. Klevin, “Asymptotics of the Helmholtz equation solutions in a two-layer medium with a localized right-hand side”, TMF, 216:1 (2023), 148–168; Theoret. and Math. Phys., 216:1 (2023), 1036–1054
Linking options:
https://www.mathnet.ru/eng/tmf10421https://doi.org/10.4213/tmf10421 https://www.mathnet.ru/eng/tmf/v216/i1/p148
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Abstract page: | 151 | Full-text PDF : | 13 | Russian version HTML: | 80 | References: | 22 | First page: | 12 |
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