Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation
Abstract
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. 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), additionally 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.
Keywords
Cite
@article{arxiv.cond-mat/0404600,
title = {Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation},
author = {Z. Rapti and P. G. Kevrekidis and A. Smerzi and A. R. Bishop},
journal= {arXiv preprint arXiv:cond-mat/0404600},
year = {2015}
}