"Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates"

One of my research papers just got published in Physica D. My collaborators and I posted a version of it on the arXiv many moons ago and, in fact, it has already been cited a couple of times.

My coauthors for this paper are Panos Kevrekidis, Boris Malomed, and Dimitri Frantzeskakis.

Here is the 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.


Basically, the idea is that the nonlinearity coefficient is periodic (which can be achieved using a spatially-periodic magnetic field) and one can get lots of interesting things by putting the periodicity there instead of in the linear potential (which has been studied in considerable detail by many people, including me).