Singularity analysis and integrability of a Burgers-type system of Foursov.
We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.
We consider the functional where is a bounded domain and is a convex function. Under general assumptions on , Crasta [Cr1] has shown that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball. With some restrictions on , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...