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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 156513, 7 pages
http://dx.doi.org/10.1155/2014/156513
Research Article

Dynamics of Bose-Einstein Condensates: Exact Representation and Topological Classification of Coherent Matter Waves

1Department of Electrical Engineering, Guilin College of Aerospace Technology, Guilin 541004, China
2School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541001, China
3School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 5 December 2013; Accepted 10 January 2014; Published 3 March 2014

Academic Editor: Dianchen Lu

Copyright © 2014 Leilei Jia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using the bifurcation theory of dynamical systems, we present the exact representation and topological classification of coherent matter waves in Bose-Einstein condensates (BECs), such as solitary waves and modulate amplitude waves (MAWs). The existence and multiplicity of such waves are determined by the parameter regions selected. The results show that the characteristic of coherent matter waves can be determined by the “angular momentum” in attractive BECs while for repulsive BECs; the waves of the coherent form are all MAWs. All exact explicit parametric representations of the above waves are exhibited and numerical simulations support the result.