Modulated Amplitude Waves in Bose-Einstein Condensates

Abstract

We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits (``modulated amplitude waves'') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations.

5 pages, 4 figs, revtex, final form of paper, to appear in PRE (forgot to include \bibliography command in last update, so this is a correction of that; the bibliography is hence present again)