A Bogomol`nyi equation for intersecting domain walls

We argue that the Wess-Zumino model with quartic superpotential admits static solutions in which three domain walls intersect at a junction. We derive an energy bound for such junctions and show that configurations saturating it preserve 1/4 supersymmetry.Comment: 4 pages revtex. No figures. Revised version to appear in Physical Review Letters includes discussion of the supersymmetry algebr

One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Switching phenomena in magnetic vortex dynamics

A magnetic nanoparticle in a vortex state is a promising candidate for the information storage. One bit of information corresponds to the upward or downward magnetization of the vortex core (vortex polarity). Generic properties of the vortex polarity switching are insensitive of the way how the vortex dynamics was excited: by an AC magnetic field, or by an electrical current. We study theoretically the switching process and describe in detail its mechanism, which involves the creation and annihilation of an intermediate vortex-antivortex pair.Comment: REVTeX, 8 pages, 2 figures; to appear in a special issue of Low Temperature Physics in memory of A.M.Kosevic

Very Regular Solutions for the Landau-Lifschitz Equation with Electric Current

We consider a model of ferromagnetic material subject to an electric current. We prove the local in time existence of very regular solutions for this model in the scale of H k spaces. In particular, we describe in detail the compatibility conditions at the boundary for the initial data