Spectra of Nonselfadjoint Eigenvalue Problems for Elliptic Systems in Mathematical Models of the Wave Propagation in Open Waveguides

• Published in: Lobachevskii journal of mathematics Vol. 39; no. 8; pp. 1117 - 1129
• Main Authors: Shestopalov, Y. V., Smolkin, E., Kuzmina, E.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-10-2018; Springer Nature B.V
• Subjects: Algebra; Analysis; Dielectric waveguides; Eigenvalues; Elliptic functions; Geometry; Mathematical analysis; Mathematical Logic and Foundations; Mathematical models; Mathematics; Mathematics and Statistics; nonlinear media; open waveguides; Probability Theory and Stochastic Processes; Propagation; singular; Sturm–Liouville; Wave propagation; open waveguides; nonlinear media; Wave propagation; singular; Sturm–Liouville
• ISSN: 1995-0802; 1818-9962; 1818-9962
• DOI: 10.1134/S1995080218080097

Statements and analysis are presented of nonselfadjoint eigenvalue problems for elliptic equations and systems, including singular Sturm–Liouville problems on the line, that arise in mathematical models of the wave propagation in open metal-dielectric waveguides. Existence of real and complex spectra are proved and their distribution is investigated for canonical structures possessing circular symmetry of boundary contours.