This article is cited in 1 paper

Multiplicity of eigenvalues in certain boundary value problems for the Helmholtz equation

V. A. Malakhov, A. V. Nazarov, A. S. Raevskii, S. B. Raevskii

Nizhny Novgorod State Technical University

Abstract: Boundary value problems for two-layer cylindrical waveguides (namely, for a circular two-layer closed waveguide and a dielectric waveguide in an unbounded medium) are considered. It is shown that the same eigenvalues determining the wave numbers of waves in the waveguides can correspond to different solutions of the boundary value problem.

Key words: adjoint solutions, complex waves, dispersion equation, eigenvalues, wave numbers, boundary value problems for Helmholtz’s equation.

UDC: 519.634

Received: 04.07.2012
Revised: 10.12.2012

DOI: 10.7868/S0044466913050104

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:5, 616–624

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