The problem of wave propagation in an inhomogeneous half space having an index of refraction which varies slowly in the horizontal coordinates and has a single maximum on the boundary of the half space (a surface waveguide) or in its interior (an interior waveguide) is solved by the method of two-scale expansions. It is shown that the method of two-scale expansions can also be applied at high frequencies if in the case of an interior waveguide ɛp ≪ 1, where ɛ is a small parameter characterizing the slow variation of the properties of the medium in horizontal directions, and p is the dimensionless frequency. In the case of a presurface waveguide for a small number m of nodes of the eigenfunction the expansion can be used without assuming slow variation of the refractive index in the horizontal coordinates; if m ∿ p, then ɛp ≪ 1.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
V. S. Buldyrev and N. S. Grigor'eva, “The method of two-scale expansions for refractive waveguides and conditions for its applicability,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,104, 33–48 (1981).
Wave Propagation and Submarine Acoustics [in Russian], Moscow (1980).
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 78–97, 1981.
About this article
Cite this article
Buldyrev, V.S., Grigor'eva, N.S. Two-scale expansions of quasinormal waves in nonregular, refractive waveguides and an estimate of their applicability at high frequencies. J Math Sci 24, 313–324 (1984). https://doi.org/10.1007/BF01086990
- Wave Propagation
- Small Parameter
- Horizontal Direction
- Half Space