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Localized States in Discrete Nonlinear Schrödinger Equations

David Cai·A. R. Bishop·Niels Grønbech-Jensen
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Abstract

A new 1-D discrete nonlinear Schrödinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The relationship between intrinsic localized states and the soliton of the Ablowitz-Ladik NLS is discussed. It is pointed out that a staggered localized state can be viewed as a particle of a {\em negative} effective mass. It is shown that staggered localized states can exist in the discrete dark NLS. The motion of localized states and Peierls-Nabarro pinning are studied.

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David Cai, A. R. Bishop, Niels Grønbech-Jensen. 1993-03-14. Localized States in Discrete Nonlinear Schrödinger Equations. https://doi.org/10.1103/physrevlett.72.591

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