Two-dimensional clusters of solitary structures in driven optical cavities.

Using analytical and numerical approaches we study clusters of the two-dimensional localized structures of light excited in the externally driven optical cavities. Stability and instability properties of clusters of two, three, and four structures are analyzed in detail. We develop a technique for calculation of the expression for the interaction potential through modified Bessel functions that has applicability going beyond the model under consideration. Qualitative differences between stability properties of triangular and square structures are found that emphasize the role of diagonal interactions in the latter.

Stability of spiralling solitary waves in Hamiltonian systems.

We present a rigorous criterion for stability of spiralling solitary structures in Hamiltonian systems incorporating the angular momentum integral and demonstrate its applicability to the spiralling of two mutually incoherent optical beams propagating in a photorefractive material.