DYNAMICS OF BREATHERS IN DISCRETE NONLINEAR SCHRODINGER MODELS

We review some recent results concerning the existence and stability o f spatially localized and temporally quasiperiodic (non-stationary) ex citations in discrete nonlinear Schrodinger (DNLS) models. In two dime nsions, we show the existence of linearly stable, stationary and non-s tationary localized vortex-like solutions. We also show that stationar y on-site localized excitations can have internal 'breathing' modes wh ich are spatially localized and symmetric. The excitation of these mod es leads to slowly decaying, quasiperiodic oscillations. Finally, we s how that for some generalizations of the DNLS equation where bistabili ty occurs, a controlled switching between stable states is possible by exciting an internal breathing mode above a threshold value. (C) 1998 Elsevier Science B.V.