We show that the two-dimensional, nonlinear Schr\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.
@article{arxiv.1008.4592,
title = {Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\"odinger Equation with Saturable Nonlinearity},
author = {Avinash Khare and Kim Ø. Rasmussen and Mogens R. Samuelsen and Avadh Saxena},
journal= {arXiv preprint arXiv:1008.4592},
year = {2010}
}