WIAS Preprint No. 362, (1997)

Spectral properties of coupled wave equations


  • Recke, Lutz
  • Schneider, Klaus R.
  • Strygin, Vadim V.

2010 Mathematics Subject Classification

  • 35P20 35L40 47D06


  • linear system of first-order partial differential equations, semiconductor laser




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 C0-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.

Appeared in

  • Z. Angew. Math. Phys., 50 (1999), No. 6, pp. 925-933.

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