We consider shapes and dynamics of semidiscrete solitons (SDSs) in the known model of the set of linearly coupled waveguides with intrinsic cubic nonlinearity. The model applies to the description of a planar array of optical fibers or of a stack of parallel planar waveguides, in the temporal and spatial domains, respectively, as well as to the self-attractive Bose-Einstein condensate (BEC) loaded into an array of parallel tunnel-coupled cigar-shaped traps. It was found previously that the interplay of the group-velocity dispersion, discrete diffraction (in the longitudinal and transverse directions, respectively), and intrinsic self-focusing gives rise to SDSs in the array. We here develop the variational approximation (VA) and additional analytical methods for the description of the SDSs, and study their mobility and collisions by means of systematic simulations. The VA and an exact solution of the linearized equation in the cores adjacent to the central one produce an accurate description for the family of stable fundamental on-site-centered SDS solutions, as well as of surface SDSs in the semi-infinite array. The VA is also presented for transversely unstable intersite-centered solitons. In simulations, the solitons are not mobile in the discrete direction (nonsoliton semidiscrete modes may be mobile across the array). Collisions between SDSs traveling in the longitudinal direction feature a threshold separating the passage and merger or destruction. The exact shape of the threshold, considered as a function of the solitons’ energy, features irregularities, while its average form is explained analytically. “Shifted” collisions between SDSs centered at adjacent cores are also studied.

• Received 8 September 2012

DOI:https://doi.org/10.1103/PhysRevA.86.043841