Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

Details Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

2008-05-06

arxiv.org/abs/0805.0761v2

Nonlinearity 21 (2008) R139-R202

Physics

Condensed Matter

Other Condensed Matter

69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new references added, fixed typos

Scientific paper

10.1088/0951-7715/21/7/R01

The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.

Affiliated with

Also associated with

No associations

Rating

Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques 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 Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-209468