Localized states in discrete nonlinear Schrödinger equations

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Abstract
A new 1D 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, including the role of discretization as a mechanism controlling collapse. It is pointed out that a staggered localized state can be viewed as a particle of a 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 also studied.
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