In this talk, I will present a PDE model to describe a laser operating at multiple frequency channels simultaneously. The model admits a variety of solutions, including localized mode-locked pulses. This PDE model can be reduced to a few ODEs, from which we recover conditions on system parameters necessary for the existence and stability of these mode- locked pulse solutions. The bifurcations through which these attracting pulse solutions become destabilized are completely characterized in terms of the physical parameters. Through this reduced ODE model, we gain a better understanding of the physical phenomena necessary to build such a laser.