Bound states of two-dimensional solitons in the discrete nonlinear Schrödinger equation

The existence and stability of bound states (BSs) of solitary excitations in the two-dimensional discrete nonlinear Schrödinger lattice are considered. Stable BSs of two or three solitons are categorized according to their vorticity S (S = 0 corresponds to ordinary pulses, while S = 1 corresponds to discrete vortex solitons). Interactions of S = 0 solitons are found to have clear particle-like characteristics, which can be very accurately predicted in the framework of the perturbation theory that we develop. Triangular bound states of three solitons are also constructed, and particle-like characteristics in their behaviour are followed in numerical experiments. Finally, stable bound states of two vortex solitons, and S = 0-1 stable complexes are constructed. For the latter state, we find a weak dependence of the interaction-generated stability eigenvalue on the distance between the two solitons.