D.E. Pelinovsky, P.G. Kevrekidis, and D.J. Frantzeskakis

Stability of discrete solitons in nonlinear Schrodinger lattices

Physica D 212, 1-19 (2005)

Abstract:
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.

Keywords:
DISCRETE NONLINEAR SCHRODINGER EQUATIONS, DISCRETE SOLITONS, EXISTENCE AND STABILITY, EIGENVALUES OF LINEARIZED OPERATORS, PERTURBATION THEORY FOR EIGENVALUES