Analytical solutions to the spin-1 Bose-Einstein condensates
arXiv:1202.3197 · doi:10.1088/0953-4075/45/21/215302
Abstract
We analytically solve the one-dimensional coupled Gross-Pitaevskii equations which govern the motion of F=1 spinor Bose-Einstein condensates. The nonlinear density-density interactions are decoupled by making use of the unique properties of the Jacobian elliptical functions. Several types of complex stationary solutions are deduced. Furthermore, exact non-stationary solutions to the time-dependent Gross-Pitaevskii equations are constructed by making use of the spin-rotational symmetry of the Hamiltonian. The spin-polarizations exhibit kinked configurations. Our method is applicable to other coupled nonlinear systems.
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References in corpus (5)
- Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
- Solitons with Cubic and Quintic Nonlinearities Modulated in Space and Time
- Dark solitons in F=1 spinor Bose--Einstein condensate
- Broken axisymmetry phase of a spin-1 ferromagnetic Bose-Einstein condensate
- Solitons in a trapped spin-1 atomic condensate
Cited by in corpus (5)
- Exact analytical soliton solutions in dipolar BEC
- Metastable spin textures and Nambu-Goldstone modes of a ferromagnetic spin-1 Bose-Einstein condensate confined in a ring trap
- Exact solutions to the spin-2 Gross-Pitaevskii equations
- Exact temporal evolution of the two-species Bose-Einstein condensates
- Fractional windings of the spinor condensates on a ring