Nonlinear Schrödinger lattices I: Stability of discrete solitons

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

Nonlinear Schrödinger lattices I: Stability of discrete solitons

Authors

Pelinovsky, D. E.

Kevrekidis, P. G.

Frantzeskakis, D. J.

Description

We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrödinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arbitrary finite superposition of {\em in-phase} or {\em 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.
21 pages, 10 figures