Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr'odinger Equation with Saturable Nonlinearity

摘要

We show that the two-dimensional, nonlinear Schr\"odinger lattice with asaturable nonlinearity admits periodic and pulse-like exact solutions. Weestablish the general formalism for the stability considerations of thesesolutions and give examples of stability diagrams. Finally, we show that theeffective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.