Selftrapping dynamics in two-dimensional nonlinear lattices

We compute numerically the selftrapping dynamics for an electron or excitat ion initially located on a single site of a two-dimensional nonlinear latti ce of arbitrary nonlinear exponent. The time evolution is given by the Disc rete Nonlinear Schrodinger (DNLS) equation and we focus on the long-time av erage probability at the initial site and the mean square displacement in t erms of both the exponent and strength of the nonlinearity. For the square and triangular nonlinear lattices, we find selftrapping for nonlinearity pa rameters greater than an exponent-dependent critical value, whose magnitude increases (decreases) with the nonlinear exponent when this is larger (sma ller) than one, approximately.