Publication Date
2007
Journal or Book Title
Physica D: Nonlinear Phenomena
Abstract
We investigate the dynamics of an effectively one-dimensional Bose–Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross–Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.
Pages
104-115
Volume
229
Issue
2
Recommended Citation
Porter, Mason A. and Kevrekidis, PG, "Modulated amplitude waves in collisionally inhomogeneous Bose–Einstein condensates" (2007). Physica D: Nonlinear Phenomena. 1099.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1099
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVK-4N7XP3P-1&_user=1516330&_coverDate=05%2F15%2F2007&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=7c2ad28648e9d0e1da353724e8f1b1b1&searchtype=a