Integrability of the Gross-Pitaevskii equation with Feshbach resonance management |
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Authors: | Dun Zhao Hong-Gang Luo Hua-Yue Chai |
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Affiliation: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China b Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000, China c Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China d Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China |
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Abstract: | In this Letter 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, A. Hasegawa, T.L. Belyaeva, Phys. Rev. Lett. 98 (2007) 074102]. 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 solitons and the dynamics of the Bose-Einstein condensates by using the Feshbach resonance technique. |
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Keywords: | 05.45.Yv 03.75.Lm 03.75.Kk |
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