Instabilities of cavity solitons in optical parametric oscillators.

Using an example of cavity solitons in optical parametric oscillators it is demonstrated that Hopf instability of these dissipative structures can be directly associated with internal modes of their conservative counterparts. The latter ones are free propagating quadratic solitons in this case. Linear stability analysis and numerical simulation also reveal multistability and complex instability induced spatiotemporal dynamics of single and multihump cavity solitons.