Horseshoes for coupled discrete nonlinear Schrödinger equations

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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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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