Dissipative soliton excitability induced by spatial inhomogeneities and drift

We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, systems which do not exhibit oscillatory dissipative solitons, including gradient systems such as the prototypical Swift-Hohenberg equation, display oscillations and Type I and II excitability when adding inhomogeneities and drift to the system. This rich dynamical behavior arises from the interplay between the pinning to the inhomogeneity and the pulling of the drift. The scenario presented here provides a general theoretical understanding
of oscillatory regimes of dissipative solitons reported in semiconductor microresonators. Our results open also the possibility to observe this phenomenon in a wide variety of physical systems.