Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes

Abstract

An analytical stability criterion for discrete solitons is presented. Its evaluation proves that discreteness reduces (in comparison with the continuum results) the critical nonlinearity parameter (which separates stable and unstable regimes). Unstable discrete solitons may "collapse" into the more stable intrinsically localized states. The theory applies to a discrete nonlinear Schr\"odinger equation, but can be generalized to other systems.