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