Abstract
We consider a mathematical model (the so-called traveling-wave system) which describes longitudinal dynamical effects in semiconductor lasers. This model consists of a linear hyperbolic system of PDEs, which is nonlinearly coupled with a slow subsystem of ODEs. We prove that a corresponding initial-boundary value problem is well posed and that it generates a smooth infinite-dimensional dynamical system. Exploiting the particular slow-fast structure, we derive conditions under which there exists a low-dimensional attracting invariant manifold. The flow on this invariant manifold is described by a system of ODEs. Mode approximations of that system are studied by means of bifurcation theory and numerical tools.
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Sieber, J., Recke, L. & Schneider, K.R. Dynamics of Multisection Semiconductor Lasers. Journal of Mathematical Sciences 124, 5298–5309 (2004). https://doi.org/10.1023/B:JOTH.0000047355.47744.18
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DOI: https://doi.org/10.1023/B:JOTH.0000047355.47744.18