Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates
arXiv:nlin/0607009 · doi:10.1016/j.physd.2007.02.012
Abstract
We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length subjected to a spatially periodic modulation, . This "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of . We transform this equation into a GP equation with 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 , are significantly more stable than their "off-site" counterparts.
25 pages, 10 figures (many with several parts), to appear in Physica D; higher resolution versions of some figures are available at http://www.its.caltech.edu/~mason/papers
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