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Nonlinear Schrödinger lattices I: Stability of discrete solitons

D. E. Pelinovsky·P. G. Kevrekidis·D. J. Frantzeskakis
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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.

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D. E. Pelinovsky, P. G. Kevrekidis, D. J. Frantzeskakis. 2004-12-07. Nonlinear Schrödinger lattices I: Stability of discrete solitons. https://arxiv.org/abs/nlin/0410005

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