The Asymptotic Behavior of the Solutions of the Wave Equation Concentrated Near the Axis of a Two-Dimensional Waveguide in an Inhomogeneous Medium

  • B. S. Buldyrev
Part of the Topics in Mathematical Physics book series (TOMP, volume 3)


The present article describes a method for the construction of the solutions of the wave equation
$$ \frac{{\partial ^2 u}} {{\partial x^2 }} + \frac{{\partial ^2 u}} {{\partial z^2 }} + \frac{{\omega ^2 }} {{c^2 (x,z)}}u = 0 $$
which describe as ω → ∞ the propagation of waves near the axis of a waveguide.


Asymptotic Behavior Wave Equation Arbitrary Constant Inhomogeneous Medium Closed Geodesic 
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Literature Cited

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    V. M. Babich and V. F. Lazutkin, “Eigenfunctions concentrated near a closed geodesic,” in: Topics in Mathematical Physics, Vol. 2, Consultants Bureau, New York (1968).Google Scholar
  2. 2.
    V. F. Lazutkin, “Construction of an asymptotic series for eigenfunctions of the ‘bouncing-ball’ type,” Trudy MIAN, Vol 95 (in press).Google Scholar
  3. 3.
    E. Kamke, Handbook of Ordinary Differential Equations ( Russian translation], IL (1950), p. 199.Google Scholar
  4. 4.
    V.A. Yakubovich, “The stability of the solutions of a system of two canonical linear equations with periodic coefficients,” Matem. Sbornik, Vol. 37 (79), 1 (1955).Google Scholar

Copyright information

© Consultants Bureau, New York 1969

Authors and Affiliations

  • B. S. Buldyrev

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