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Modulational and Parametric Instabilities of the Discrete Nonlinear Schrödinger Equation

Z. Rapti·P. G. Kevrekidis·A. Smerzi·A. R. Bishop
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Abstract

We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{ö}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.

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Z. Rapti, P. G. Kevrekidis, A. Smerzi, A. R. Bishop. 2004-04-25. Modulational and Parametric Instabilities of the Discrete Nonlinear Schrödinger Equation. https://doi.org/10.1088/0953-4075%2F37%2F7%2F070

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