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Skyrmions in Gross-Pitaevskii functionals. (English) Zbl 1212.35127

Summary: In Bose-Einstein condensates (BECs), skyrmions can be characterized by pairs of linking vortex rings coming from two-component wave functions. Here we construct skyrmions by studying critical points of Gross-Pitaevskii functionals with two-component wave functions. Using localized energy method, we rigorously prove the existence, and describe the configurations of skyrmions in such BECs.

MSC:

35J60 Nonlinear elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35B25 Singular perturbations in context of PDEs
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