Two-dimensional soliton families in saturable quasi-nonlinear lattices

In this work, we demonstrate the stabilization of two-dimensional soliton families, including fundamental solitons and soliton clusters, in the nonlinear Schrödinger equation with the nonlinearity arranged as a saturable quasi-nonlinear lattice. We discover interesting properties of these families by presenting their intensity profiles, powers, amplitudes, and perturbed propagations. The most interesting finding is their improved stability, as compared to the case of a Kerr (cubic) nonlinear lattice. The radii of both fundamental solitons and soliton clusters decrease with the propagation constant, while the amplitudes increase. Curiously, the power of these solitons and clusters always increases with the propagation constant, rising sharply when the propagation constant approaches its critical value. Furthermore, the critical propagation constant decreases as the saturation parameter increases. In addition to studying the perturbed propagation of these waves, we also investigate the propagation under a dynamically modulated saturation parameter.