Stability of strongly localized excitations in discrete media with cubic nonlinearity

Abstract

By using a linear analysis it is analytically shown that the stability of strongly localized modes depends on their symmetry, the sign of nonlinearity, and the degree of localization. The existence of a stable, bright, even mode of the discrete nonlinear Schrödinger equation is demonstrated and confirmed by direct numerical simulations. Possible applications to all-optical switching are discussed.