Interaction of oscillatory and excitable dissipative solitons in a nonlinear optical cavity

Dissipative solitons (DS) are localized states that appear in systems driven
out of equilibrium. The interaction of stationary DS has long been studied, but they
may also undergo a number of instabilities leading to more complicated dynami-
cal regimes. In this case, the effects of the interaction are much less known. Here
we address the problem of the interaction between oscillatory and excitable dissipa-
tive solitons in a Kerr cavity. These oscillatory structures can be considered as non
punctual oscillators with a highly non-trivial spatial coupling, which leads to rather
complicated dynamics beyond what can be explained in terms of simple coupled
oscillators. We also explore the possibility of using coupled excitable DS to build
all-optical logical gates.