Localized states in discrete nonlinear Schrödinger equations
David CaiTheoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545A. R. BishopTheoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545Niels Grønbech‐JensenTheoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
1994en
ABI
Abstract
A new 1D discrete nonlinear Schr\"odinger (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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