EXACT SOLUTIONS TO THE SPIN-2 GROSS–PITAEVSKII EQUATIONS
2012 ◽
Vol 27
(02)
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pp. 1350013
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Keyword(s):
The One
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We present several exact solutions to the coupled nonlinear Gross–Pitaevskii equations which describe the motion of the one-dimensional spin-2 Bose–Einstein condensates. The nonlinear density–density interactions are decoupled by making use of the properties of Jacobian elliptical functions. The distinct time factors in each hyperfine state implies a "Lamor" procession in these solutions. Furthermore, exact time-evolving solutions to the time-dependent Gross–Pitaevskii equations are constructed through the spin-rotational symmetry of the Hamiltonian. The spin-polarizations and density distributions in the spin-space are analyzed.
2012 ◽
Vol 67
(3-4)
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pp. 141-146
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2005 ◽
Vol 50
(8-9)
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pp. 1345-1362
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2006 ◽
Vol 20
(15)
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pp. 2189-2221
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2003 ◽
Vol 36
(6)
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pp. 1615-1621
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1977 ◽
Vol 89
(2)
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pp. 265-303
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1994 ◽
Vol 73
(4)
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pp. 305-317
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