Stability of discrete solitons in nonlinear Schrodinger lattices

We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrodinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arbitrary finite superposition of in-phase or anti-Phase excited nodes, separated by an arbitrary sequence of empty nodes. By using stability analysis, we prove that the discrete solitons are all unstable near the anti-continuum limit, except for the solitons, which consist of alternating anti-phase excited nodes. We classify analytically and confirm numerically the number of unstable eigenvalues associated with each family of the discrete solitons. (c) 2005 Elsevier B.V. All rights reserved.