Curvature stabilized skyrmions with angular momentum

We examine skyrmionic field configurations on a spherical ferromagnet with large normal anisotropy. Exploiting variational concepts of angular momentum we find a new family of localized solutions to the Landau-Lifshitz equation that are topologically distinct from the ground state and not equivariant. Significantly, we observe an emergent spin-orbit coupling on the level of magnetization dynamics in a simple system without individual rotational invariance in spin and coordinate space

Near Resonant Approximation of the Rotating Stratified Boussinesq system on a 3-Torus

Based on a novel treatment of near resonances, we introduce a new approximation for the rotating stratified Boussinesq system on three-dimensional tori with arbitrary aspect ratios. The rotation and stratification parameters are arbitrary and not equal. We obtain global existence for the proposed nonlinear system for arbitrarily large initial data. This system is sufficiently accurate, with an important feature of coupling effects between slow and fast modes. The key to global existence is a sharp counting of the relevant number of nonlinear interactions. An additional regularity advantage arises from a careful examination of some mixed type interaction coefficients. In a wider context, the significance of our near resonant approach is a delicate balance between the inclusion of more interacting modes and the improvement of regularity properties, compared to the well-studied singular limit approach based on exact resonance