Analytical solutions to the spin-1 Bose-Einstein condensates
Zhi-Hai Zhang, Cong Zhang, Shi-Jie Yang, Shiping Feng
TL;DR
This paper provides analytical solutions to the coupled Gross-Pitaevskii equations for one-dimensional spin-1 Bose-Einstein condensates, revealing complex stationary and non-stationary states using Jacobian elliptic functions.
Contribution
It introduces a novel analytical approach to solve coupled nonlinear equations in spinor Bose-Einstein condensates, including exact non-stationary solutions leveraging spin-rotational symmetry.
Findings
Derived complex stationary solutions using Jacobian elliptic functions
Constructed exact non-stationary solutions with kinked spin-polarizations
Method applicable to other coupled nonlinear systems
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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