ON LOCALIZATION IN THE DISCRETE NONLINEAR SCHRODINGER-EQUATION

For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits localization in regimes where blow-up cannot occur in the continuum system. This phenomenon is investigated numerically, and the grid resolution at which the transition occurs is determined.