Physica D 213 (1):
98--112 (January 2006)The traveling wave model consisting of a hyperbolic system of linear first order PDE's nonlinearly coupled with a system of ODE's is used to model the dynamics of multisection semiconductor lasers. It is shown how low dimensional systems of ODE's based on the projection of the original system into the subspace spanned only by a few instantaneously changing spectral elements allow a precise approximation of the original model. The constructed low dimensional Mode Approximation systems are accessible to classical bifurcation analysis and numerical tools. The presented method is applied to characterise quasi-periodic orbits arising in a three section distributed feedback laser. The obtained results are highly important for tailoring such pulsating lasers to be applied in optical communication systems..