The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz's equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width 1 and 1 - epsilon, where epsilon > 0 is a small parameter. The width function of the part of the waveguide connecting these outlets is of order root epsilon; it is defined as a linear combination of three fairly arbitrary functions, whose coefficients are obtained from a certain nonlinear equation. The result is derived from an asymptotic analysis of an auxiliary object, the augmented scattering matrix.

Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide

Cardone G;
2012-01-01

Abstract

The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz's equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width 1 and 1 - epsilon, where epsilon > 0 is a small parameter. The width function of the part of the waveguide connecting these outlets is of order root epsilon; it is defined as a linear combination of three fairly arbitrary functions, whose coefficients are obtained from a certain nonlinear equation. The result is derived from an asymptotic analysis of an auxiliary object, the augmented scattering matrix.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12070/4055
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