D.E. Pelinovsky, P.G. Kevrekidis, and D.J. Frantzeskakis
Stability of discrete solitons in nonlinear Schrodinger lattices
Physica D 212, 1-19 (2005)
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.
DISCRETE NONLINEAR SCHRODINGER EQUATIONS, DISCRETE SOLITONS,
EXISTENCE AND STABILITY, EIGENVALUES OF LINEARIZED OPERATORS, PERTURBATION THEORY FOR EIGENVALUES