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Longtime behavior of the coupled traveling wave model for semiconductor lasers

Research output: Working paperWorking paper and Preprints

  • J Sieber
Original languageEnglish
Publication date2003
StateUnpublished

Abstract

The coupled traveling wave model is a popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. This model consists of a hyperbolic linear system of partial differential equations with one spatial dimension, which is nonlinearly coupled with a slow subsystem of ordinary differential equations. We first prove the basic statements about the existence of solutions of the initial-boundary-value problem and their smooth dependence on initial values and parameters. Hence, the model constitutes a smooth infinite-dimensional dynamical system. Then we exploit this fact and the particular slow-fast structure of the system to construct a low-dimensional attracting invariant manifold for certain parameter constellations. The flow on this invariant manifold is described by a system of ordinary differential equations that is accessible to classical bifurcation theory and numerical tools like such as AUTO.

Additional information

Additional information: Preprint submitted to Elsevier Science Sponsorship: The research of J.S. was partially supported by the the Collaborative Research Center 555 "Complex Nonlinear Processes" of the Deutsche Forschungsgemeinschaft (DFG), and by EPSRC grant GR/R72020/01. The author thanks Mark Lichtner and Bernd Krauskopf for discussions and their helpful suggestions.

Research areas

  • laser dynamics, strongly continuous semigroup

Documents

Documents

  • 2003r23

    Preprint (usually an early version) , 431 KB, PDF-document

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