Geodesic
Dynamics of Multisection Semiconductor Lasers
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 2, Tome 2 (2003), pp. 70-82

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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. 
@article{CMFD_2003_2_a3,
     author = {J. Sieber and L. Recke and K. R. Schneider},
     title = {Dynamics of {Multisection} {Semiconductor} {Lasers}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {70--82},
     publisher = {mathdoc},
     volume = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2003_2_a3/}
}
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J. Sieber; L. Recke; K. R. Schneider. Dynamics of Multisection Semiconductor Lasers. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 2, Tome 2 (2003), pp. 70-82. http://geodesic.mathdoc.fr/item/CMFD_2003_2_a3/