Horseshoes for coupled discrete nonlinear Schrödinger equations

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we study the spatial disorder of coupled discrete nonlinear Schrödinger (CDNLS) equations with piecewise-monotone nonlinearities. By the construction of horseshoes, we show that the CDNLS equation possesses a hyperbolic invariant Cantor set on which it is topological conjugate to the full shift on N symbols. The CDNLS equation exhibits spatial disorder, resulting from the strong amplitudes and stiffness of the nonlinearities in the system. The complexity of the disorder is determined by the oscillations of the nonlinearities. We then apply our results to CDNLS equations with Kerr-like nonlinearity. We shall also show some patterns of the localized solutions of the CDNLS equation.

Original languageEnglish
Article number022701
JournalJournal of Mathematical Physics
Volume50
Issue number2
DOIs
Publication statusPublished - 2009 Mar 9

Fingerprint

Horseshoe
Discrete Equations
nonlinear equations
Nonlinear Equations
nonlinearity
Nonlinearity
Disorder
disorders
Cantor set
Invariant Set
stiffness
Stiffness
Monotone
Oscillation
oscillations
shift

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Horseshoes for coupled discrete nonlinear Schrödinger equations. / Shieh, Shih-Feng.

In: Journal of Mathematical Physics, Vol. 50, No. 2, 022701, 09.03.2009.

Research output: Contribution to journalArticle

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