Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

David Cai, A. R. Bishop, Niels Grønbech-Jensen

Research output: Contribution to journalArticle

Abstract

In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schrödinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution.

Original languageEnglish (US)
JournalPhysical Review E
Volume52
Issue number6
DOIs
StatePublished - 1995

Fingerprint

Breathers
Excitation
solitary waves
Multiple-soliton Solutions
Discrete Breathers
continuums
excitation
inverse scattering
Nonlinear Lattice
Inverse Scattering Transform
Time-periodic Solutions
Lattice System
Continuum Limit
Solitons
Continuum
Nonlinear Systems
Exact Solution

ASJC Scopus subject areas

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

Cite this

Spatially localized, temporally quasiperiodic, discrete nonlinear excitations. / Cai, David; Bishop, A. R.; Grønbech-Jensen, Niels.

In: Physical Review E, Vol. 52, No. 6, 1995.

Research output: Contribution to journalArticle

Cai, David ; Bishop, A. R. ; Grønbech-Jensen, Niels. / Spatially localized, temporally quasiperiodic, discrete nonlinear excitations. In: Physical Review E. 1995 ; Vol. 52, No. 6.
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