  Coupled wave equations are popular tool for investigating longitudinal
dynamical effects in semiconductor lasers, for example, sensitivity to delayed
optical feedback. We study a model that 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 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 such as AUTO.
