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Two-scale expansions of quasinormal waves in nonregular, refractive waveguides and an estimate of their applicability at high frequencies

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Abstract

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.

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Literature cited

  1. 1.

    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).

  2. 2.

    Wave Propagation and Submarine Acoustics [in Russian], Moscow (1980).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 78–97, 1981.

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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

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Keywords

  • Wave Propagation
  • Refraction
  • Small Parameter
  • Horizontal Direction
  • Half Space