Spectral Theory pp 1-23 | Cite as

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

Chapter

## Abstract

The present article describes a method for the construction of the solutions of the wave equation
which describe as

$$ \frac{{\partial ^2 u}}
{{\partial x^2 }} + \frac{{\partial ^2 u}}
{{\partial z^2 }} + \frac{{\omega ^2 }}
{{c^2 (x,z)}}u = 0 $$

(1)

*ω*→ ∞ the propagation of waves near the axis of a waveguide.## Keywords

Asymptotic Behavior Wave Equation Arbitrary Constant Inhomogeneous Medium Closed Geodesic
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Literature Cited

- 1.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.V. F. Lazutkin, “Construction of an asymptotic series for eigenfunctions of the ‘bouncing-ball’ type,” Trudy MIAN, Vol 95 (in press).Google Scholar
- 3.E. Kamke, Handbook of Ordinary Differential Equations ( Russian translation], IL (1950), p. 199.Google Scholar
- 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