We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non-autonomous model. It can be shown that a C 0 semigroup on L ∞ has a bounded generator [5].WELL-POSEDNESS, SMOOTH DEPENDENCE AND CENTRE MANIFOLD REDUCTION 933 models, we are dealing with, such properties are proved in some exceptional cases only. This has been resolved recently in [8,9,17] for a general class of semilinear hyperbolic systems.On the other hand, it turns out the following: if the coefficients are sufficiently smooth with respect to time then all the interesting dynamics, which is observable in numerical and real world experiments, can be rigorously described by our general models. It occurs on exponentially attracting invariant manifolds of continuous functions. Such solutions do not possess jumps in space due to discontinuities of the initial data or to incompatible boundary data as discussed, e.g. in [18].Let us shortly discuss some related results: Jochmann and Recke [19] got existence and uniqueness of weak solutions under the assumption that the coupled travelling wave equations are linear with respect to the light amplitudes. They did not deal with smooth dependence of the solutions on the initial data.Peterhof and Sandstede [13] and Sieber [12,15] also assumed the coupled travelling wave equation to be linear, and, moreover, they considered a Galerkin projected version of the carrier rate equation. In this setting the equations are linear with respect to the infinite-dimensional state parameter (the space-dependent light amplitudes) and really non-linear only with respect to the remaining finite-dimensional state parameter (the carrier densities, which are piecewise constant in space). Hence, the state space for the light amplitudes could be chosen as a 'large' L 2 space, and, nevertheless, the authors rigorously got smooth semiflows and a rich bifurcation behaviour. Remark that in this setting the spectrum determined exponential dichotomy of the linearized semiflow is known due to a result of Neves, Ribeiro and Lopes [20].Renardy [14] and Haken and Renardy [21] considered not edge emitting, but ring lasers. Thus the spatial domain is not an interval, but a circle, and the Nemytskij operators map the 'small' space of continuously differentiable functions on the circle into itself.Similarly Illner and Reed [22] and Vanderbauwhede and Iooss [23, Section 4, Example 3] considered semilinear hyperbolic initial boundary value problems (not related to laser dynamics), where the non-linearities are compatible with the bo...