Nonlinear Schrödinger lattices I: Stability of discrete solitons

Abstract

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

Cited by in corpus (1)

• Nonlinear Schrödinger lattices II: Persistence and Stability of Discrete Vortices