A. Aslanyan, L. Parnovski, D. Vassiliev
Complex resonances in acoustic waveguides
(259K, Gzipped postscript)
ABSTRACT. We consider a two-dimensional infinitely long acoustic waveguide
formed by two parallel lines containing an arbitrarily shaped
obstacle. The existence of trapped modes that are the eigenfunctions
of the Laplace operator in the corresponding domain subject to
Neumann boundary conditions was proved by Evans, Levitin & Vassiliev
(1994) for obstacles symmetric about the centreline of the waveguide.
In our paper we deal with the situation when the obstacle is shifted
with respect to the centreline and study the resulting complex
resonances. We are particularly interested in those resonances which
are perturbations of (real) eigenvalues. We study how an eigenvalue
becomes a complex resonance moving from the real axis into the upper
half--plane as the obstacle is shifted from its original position.
The shift of the eigenvalue along the imaginary axis is predicted
theoretically and the result is compared with numerical computations.
The total number of resonances lying inside a sequence of expanding
circles is also calculated numerically.