2001/11/06 by P. G. Kevrekidis, P G Kevrekidis, Boris A. Malomed +3 · 4 citations
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · doi:10.1088/0305-4470/34/45/302
openalex publication_date 2001/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.