Localized States in Discrete Nonlinear Schrödinger Equations

Details Localized States in Discrete Nonlinear Schrödinger Equations Localized States in Discrete Nonlinear Schrödinger Equations

1993-03-14

arxiv.org/abs/patt-sol/9305003v1

Nonlinear Sciences

Pattern Formation and Solitons

LaTeX file. Two postscript figure files

Scientific paper

10.1103/PhysRevLett.72.591

A new 1-D discrete nonlinear Schr\"{o}dinger (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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