Parametric and modulational instabilities of the discrete nonlinear Schrödinger equation

Z. Rapti, P. G. Kevrekidis, A. Smerzi, A. R. Bishop

Research output: Contribution to journalArticlepeer-review


We examine the parametric and modulational instabilities arising in a non-autonomous, discrete nonlinear Schrödinger equation. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), in addition to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its principal dynamical characteristic is that, typically, it develops over much larger times than the modulational instability, a feature that is qualitatively justified by comparison of the corresponding instability growth rates.

Original languageEnglish (US)
Pages (from-to)S257-S264
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Issue number7
StatePublished - Apr 14 2004
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics


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