SMALL-AMPLITUDE EXCITATIONS IN A DEFORMABLE DISCRETE NONLINEAR SCHRODINGER-EQUATION

A detailed analysis of the small-amplitude solutions of a deformed dis crete nonlinear Schrodinger equation is performed. For generic deforma tions the system possesses ''singular'' points which split the infinit e chain in a number of independent segments. We show that small-amplit ude dark solitons in the vicinity oi the singular points are described by the Toda-lattice equation while away from the singular points they are described by the Korteweg-de Vries equation. Depending on the val ue of the deformation parameter and of the background level several ki nds of solutions are possible. In particular, we delimit the regions i n the parameter space in which dark solitons are stable in contrast wi th regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidl y spreading solutions may exist.