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arXiv · 1209.5852

Exact solutions to the spin-2 Gross-Pitaevskii equations

Zhi-Hai Zhang·Yong-Kai Liu·Shi-Jie Yang
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Abstract

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.

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Zhi-Hai Zhang, Yong-Kai Liu, Shi-Jie Yang. 2012-09-26. Exact solutions to the spin-2 Gross-Pitaevskii equations. https://doi.org/10.1142/s0217984913500139

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