Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system

V. V. Konotop, David Cai, M. Salerno, A. R. Bishop, Niels Grønbech-Jensen

Research output: Contribution to journalArticle

Abstract

We develop a comprehensive perturbation theory for the inhomogeneous, discrete one-dimensional nonlinear Schrödinger equation based on the inverse scattering transform. We also discuss single-soliton dynamics within the adiabatic approximation and derive higher order corrections to this approximation. Using this perturbation theory, we study in detail the motion of a soliton interacting with a point impurity, either nondissipative or dissipative, in the presence of a spatially linear potential. We predict that there are two kinds of dynamical localization of a soliton in the presence of the nondissipative impurity, depending on the impurity strength. One is the usual dynamical localization, which is qualitatively the same as the one in the absence of the impurity, and the other is the pinning of a soliton by an impurity of sufficient strength. The predictions of these phenomena and their various dynamical properties are confirmed by numerical simulations of the full system.

Original languageEnglish (US)
Pages (from-to)6476-6485
Number of pages10
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number6 SUPPL. B
StatePublished - Jun 1996

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nonlinear systems
Impurities
Discrete Systems
Solitons
Nonlinear Systems
solitary waves
impurities
Interaction
Perturbation Theory
interactions
perturbation theory
Inverse Scattering Transform
inverse scattering
Approximation
approximation
nonlinear equations
Nonlinear Equations
Higher Order
Sufficient
Predict

ASJC Scopus subject areas

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

Cite this

Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system. / Konotop, V. V.; Cai, David; Salerno, M.; Bishop, A. R.; Grønbech-Jensen, Niels.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 53, No. 6 SUPPL. B, 06.1996, p. 6476-6485.

Research output: Contribution to journalArticle

Konotop, V. V. ; Cai, David ; Salerno, M. ; Bishop, A. R. ; Grønbech-Jensen, Niels. / Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system. In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 1996 ; Vol. 53, No. 6 SUPPL. B. pp. 6476-6485.
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