Modulated amplitude waves in Bose-Einstein condensates.

We analyze spatiotemporal 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.