Rotating matter waves in Bose-Einstein condensates. (English) Zbl 1124.35085
Summary: We consider analytically and numerically the dynamics of waves in two-dimensional, magnetically trapped Bose-Einstein condensates in the weak interaction limit. In particular, we consider the existence and stability of azimuthally modulated structures such as rings, multi-poles, soliton necklaces, and vortex necklaces. We show how such structures can be constructed from the linear limit through Lyapunov-Schmidt techniques and continued to the weakly nonlinear regime. Subsequently, we examine their stability, and find that among the above solutions the only one which is always stable is the vortex necklace. The analysis is given for both attractive and repulsive interactions among the condensate atoms. Finally, the analysis is corroborated by numerical bifurcation results, as well as by numerical evolution results that showcase the manifestation of the relevant instabilities.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 82D50 | Statistical mechanics of superfluids |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 37K45 | Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems |
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