Curved vortex surfaces in four-dimensional superfluids. II. Equal-frequency double rotations

As is well known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices, respectively. Recently, we have studied how, in a hypothetical four-dimensional (4D) superfluid, such excitations can be generalized to vortex planes and surfaces. In this paper we continue our analysis of skewed and curved vortex surfaces based on the 4D Gross-Pitaevskii equation and show that certain types of such states can be stabilized by equal-frequency double rotations for suitable parameters. This work extends the rich phenomenology of vortex surfaces in four dimensions and raises interesting questions about vortex reconnections and the competition between various vortex structures which have no direct analog in lower dimensions.