Modulational and Parametric Instabilities of the Discrete Nonlinear Schrödinger Equation

Details Modulational and Parametric Instabilities of the Discrete Nonlinear Schrödinger Equation Modulational and Parametric Instabilities of the Discrete Nonlinear Schrödinger Equation

2004-04-25

arxiv.org/abs/cond-mat/0404600v1

J. Phys. B: At. Mol. Opt. Phys. 37, (2004) S257-S264

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

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.

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