Scheme for interpretation of approximately computed eigenvalues embedded in a continuous spectrum

作者：Nazarov S A^*

来源：Computational Mathematics and Mathematical Physics, 2013, 53(6): 702-720.

DOI：10.1134/S0965542513060122

• acoustic waveguide
• approximate computation of an eigenvalue in the continuous spectrum
• enforced stability
• augmented scattering matrix

It is assumed that a trapped mode (i.e., a function decaying at infinity that leaves small discrepancies of order E %26gt; a parts per thousand(a) 1 in the Helmholtz equation and the Neumann boundary condition) at some frequency kappa(0) is found approximately in an acoustic waveguide Omega(0). Under certain constraints, it is shows that there exists a regularly perturbed waveguide Omega(E %26gt;) with the eigenfrequency kappa(E %26gt;) = kappa(0) + O(E %26gt;). The corresponding eigenvalue lambda(E %26gt;) of the operator belongs to the continuous spectrum and, being naturally unstable, requires %26quot;fine tuning%26quot; of the parameters of the small perturbation of the waveguide wall. The analysis is based on the concepts of the augmented scattering matrix and the enforced stability of eigenvalues in the continuous spectrum.

• 出版日期2013-6