Analytic vortices and magnetic resonances in rotating superfluidHe3−A

We study theoretically three types of analytic vortices in rotating superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}-A$. We have shown that in the Ginzburg-Landau regime and in an axial magnetic field the circular and the hyperbolic vortices form a stable two-dimensional lattice. We study also the spinwave spectra associated with these three types of vortices. We find that the radial vortex gives rise to the transverse satellite resonance consistent with a recent NMR experiment in rotating ${}_{}{}^3{}_{}{}^{}\mathrm{He}-A$ by Hakonen et al. However, the absence of other satellite resonances is quite puzzling.