Parametric and modulational instabilities of the discrete nonlinear Schrödinger equation

Z Rapti, P G Kevrekidis, A Smerzi, A R Bishop
2004 Journal of Physics B: Atomic, Molecular and Optical Physics  
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schrödinger 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.
more » ... 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.
doi:10.1088/0953-4075/37/7/070 fatcat:t2wxnptzrfeyhcxlghjyxhwumu