Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2008-08-28
Phys. Lett. A 372, 5644 (2008)
Nonlinear Sciences
Pattern Formation and Solitons
13 pages
Scientific paper
10.1016/j.physleta.2008.07.013
In this paper we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross-Pitaevskii equation is completely integrable. Under the present model, this integrability condition is completely consistent with that proposed by Serkin, Hasegawa, and Belyaeva [V. N. Serkin et al., Phys. Rev. Lett. 98, 074102 (2007)]. Furthermore, this integrability can also be explicitly shown by a transformation, which can convert the Gross-Pitaevskii equation into the well-known standard nonlinear Schr\"odinger equation. By this transformation, each exact solution of the standard nonlinear Schr\"odinger equation can be converted into that of the Gross-Pitaevskii equation, which builds a systematical connection between the canonical solitons and the so-called nonautonomous ones. The finding of this transformation has a significant contribution to understanding the essential properties of the nonautonomous solitions and the dynamics of the Bose-Einstein condensates by using the Feshbach resonance technique.
Chai Hua-Yue
Luo Hong-Gang
Zhao Dun
No associations
LandOfFree
Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management 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 Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-327152