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 lowdimensional
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.