Adiabatic approximation of the green function of the Helmholtz operator in almost stratified medias

R. M. Perez; V. Rabinovich; I. M. Sanchez

doi:10.1134/S1061920807020094

Adiabatic approximation of the green function of the Helmholtz operator in almost stratified medias

R. M. Perez, V. Rabinovich, I. M. Sanchez

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

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4 Scopus citations

Abstract

The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained.

Original language	English
Pages (from-to)	201-212
Number of pages	12
Journal	Russian Journal of Mathematical Physics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1134/S1061920807020094
State	Published - Jun 2007

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title = "Adiabatic approximation of the green function of the Helmholtz operator in almost stratified medias",

abstract = "The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained.",

author = "Perez, {R. M.} and V. Rabinovich and Sanchez, {I. M.}",

note = "Funding Information: The work was supported by CONACYT project # 43432. The authors are grateful to Professor V. Kucherenko for useful discussions and valuable remarks.",

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AU - Perez, R. M.

AU - Rabinovich, V.

AU - Sanchez, I. M.

N1 - Funding Information: The work was supported by CONACYT project # 43432. The authors are grateful to Professor V. Kucherenko for useful discussions and valuable remarks.

PY - 2007/6

Y1 - 2007/6

N2 - The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained.

AB - The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained.

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DO - 10.1134/S1061920807020094

M3 - Artículo

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VL - 14

SP - 201

EP - 212

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

IS - 2

ER -

Adiabatic approximation of the green function of the Helmholtz operator in almost stratified medias

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