DISCRETE LOCALIZED STATES AND LOCALIZATION DYNAMICS IN DISCRETE NONLINEAR SCHRODINGER-EQUATIONS

Dynamics of two-dimensional discrete structures is studied in the fram ework of the generalized two-dimensional discrete nonlinear Schrodinge r equation. The nonlinear coupling in the form of the Ablowitz-Ladik n onlinearity is taken into account. Stability properties of the station ary solutions are examined. The importance of the existence of stable immobile solitons in the two-dimensional dynamics of the travelling pu lses is demonstrated. The process of forming narrow states from initia lly broad standing or moving excitations through the quasi-collapse me chanism is analyzed. The typical scenario of the two-dimensional quasi -collapse of a moving intense pulse is the formation of pinned narrow spikes.