Influence of geometry of waveguide arrays to get discrete solitons

Based on the numerical experiment techniques, we addressed this work to the study of the physical parameters, which allow the discrete soliton formation and propagation in two dimensional waveguide arrays of different geometries. The mathematical model is based on the two dimensional nonlinear Schrödinger equation, and from the boundary conditions we are able to conclude that the array geometry plays an important role in the energy demands for the discrete soliton formation and propagation over distances of hundreds of diffraction lengths. Furthermore, our results are consistent even in the case when we take into account coupling of higher orders.