Nonlinear Schrödinger lattices I: Stability of discrete solitons
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abstract
We consider the discrete solitons bifurcating from the anti-continuum limit
of the discrete nonlinear Schr\"{o}dinger (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.
