Spectral properties of coupled wave operators

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 50; no. 6; pp. 925 - 933
• Main Authors: Recke, L., Strygin, V. V.
• Format: Journal Article
• Language: English
• Published: 01.11.1999
• ISSN: 0044-2275
• DOI: 10.1007/s000330050186

Essential features of two-section DFB semiconductor lasers can be described by a boundary value problem for the so-called coupled wave equations, a linear hyperbolic system of first order partial differential equations with piecewise constant coefficients. In this paper we investigate spectral properties of an operator H defined by this boundary value problem. We prove that H generates a C(0)-group of bounded operators in a suitable Hilbert space U, that all but finitely many eigenvalues of H are simple and have negative real parts, and that there exists a basis in U consisting of root functions of H, where all but finitely many of these root functions are eigenfunctions. (Author)