DYNAMICS IN DISCRETE 2-DIMENSIONAL NONLINEAR SCHRODINGER-EQUATIONS INTHE PRESENCE OF POINT-DEFECTS

The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrod inger equation. The nonlinear coupling in the form of the Ablowitz-Lad ik nonlinearity and point impurities is taken into account. The stabil ity properties of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-di mensional dynamics of the traveling pulses is demonstrated. The typica l scenario of the two-dimensional quasicollapse of a moving intense pu lse represents the formation of standing trapped narrow spikes. The in fluence of the point impurities on this dynamics is also investigated.