Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2004-06-26
Nonlinear Sciences
Pattern Formation and Solitons
30 pages, 5 color figures (some with multiple parts), to appear in SIAM Journal on Applied Dynamical Systems; expanded work on
Scientific paper
10.1137/040610611
We consider the Gross-Pitaevskii (GP) equation in the presence of periodic and quasiperiodic superlattices to study cigar-shaped Bose-Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice wavenumber as well as ultrasubharmonic resonances that result from interactions of both wavenumbers of the superlattice. In each case, we determine the resulting system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding solutions by direct simulations of the GP equation, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust, spatio-temporally periodic patterns.
Kevrekidis Panagiotis G.
Porter Mason A.
No associations
LandOfFree
Bose-Einstein Condensates in Superlattices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bose-Einstein Condensates in Superlattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bose-Einstein Condensates in Superlattices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-706492