Spatial properties of integrable and nonintegrable discrete nonlinear Schrödinger equations

D. Hennig, N. G. Sun, H. Gabriel, G. P. Tsironis

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

We study the spatial properties of a nonlinear discrete Schrödinger equation introduced by Cai, Bishop, and Gro/nbech-Jensen [Phys. Rev. Lett. 72, 591 (1994)] that interpolates between the integrable Ablowitz-Ladik equation and the nonintegrable discrete nonlinear Schrödinger equation. We focus on the stationary properties of the interpolating equation and analyze the interplay between integrability and nonintegrability by transforming the problem into a dynamical system and investigating its Hamiltonian structure. We find explicit parameter regimes where the corresponding dynamical system has regular trajectories leading to propagating wave solutions. Using the anti-integrable limit, we show the existence of breathers. We also investigate the wave transmission problem through a finite segment of the nonlinear lattice and analyze the regimes of regular wave transmission. By analogy of the nonlinear lattice problem with chaotic scattering systems, we find the chain lengths at which reliable information transmission via amplitude modulation is possible.

Original languageEnglish
Pages (from-to)255-269
Number of pages15
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume52
Issue number1
DOIs
Publication statusPublished - 1995
Externally publishedYes

Fingerprint

Discrete Equations
nonlinear equations
Nonlinear Lattice
Nonlinear Equations
dynamical systems
Dynamical system
Non-integrability
Amplitude Modulation
Transmission Problem
Breathers
Hamiltonian Structure
data transmission
Integrability
Analogy
Interpolate
Scattering
trajectories
Trajectory
scattering

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Spatial properties of integrable and nonintegrable discrete nonlinear Schrödinger equations. / Hennig, D.; Sun, N. G.; Gabriel, H.; Tsironis, G. P.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 52, No. 1, 1995, p. 255-269.

Research output: Contribution to journalArticle

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