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arXiv · 0808.3865

Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management

Dun Zhao·Hua-Yue Chai·Hong-Gang Luo
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Abstract

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 Schrödinger equation. By this transformation, each exact solution of the standard nonlinear Schrödinger 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.

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Dun Zhao, Hua-Yue Chai, Hong-Gang Luo. 2008-08-28. Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management. https://doi.org/10.1016/j.physleta.2008.07.013

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