Symplectic structure-preserving integrators for the two-dimensional Gross-Pitaevskii equation for BEC |
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| Authors: | Linghua Kong Jialin HongJing Chen |
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| Institution: | a School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, Chinab State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, P.O. Box 2719, Beijing, 100190, Chinac Nanchang Institute of Science & Technology, Basic Teachering Department, Nanchang, Jiangxi, 330108, Chinad School of Science, Jiangxi Agriculture University, Nangchang, Jiangxi, 330011, China |
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| Abstract: | Symplectic integrators have been developed for solving the two-dimensional Gross-Pitaevskii equation. The equation is transformed into a Hamiltonian form with symplectic structure. Then, symplectic integrators, including the midpoint rule, and a splitting symplectic scheme are developed for treating this equation. It is shown that the proposed codes fulfill the discrete charge conservation law. Furthermore, the global error of the numerical solution is theoretically estimated. The theoretical analysis is supported by some numerical simulations. |
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| Keywords: | 65Mxx |
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