Localized structures in a Kerr medium: temporal instabilities and excitability

In this work we have characterized the temporal instabilities occurring in localized structures appearing subcritically in a nonlinear Kerr medium.
The localized structures regime exhibits a transition to self-pulsation by changing a parameter.
Further change of the same parameter leads to a transition in which the oscillating state disappears, decaying to the homogeneous state in a saddle-loop bifurcation, in which the oscillation is the homoclinic orbit of a saddle point. In this state the system exhibits excitable behavior, different in some aspects to the well-known excitable behavior in the FHN equation,
being the threshold the stable manifold of the saddle.

The work has been done in collaboration with Damia Gomila and Pere Colet.