Abstract

The talk will describe some recent work on arrays of 3d topological solitons, in two different systems. The first is static Yang-Mills-Higgs monopoles (an integrable system of PDEs), and specifically doubly-periodic solutions (monopole domain walls). A few explicit solutions of this type are known; and various analytic techniques, such as the generalized Nahm transform, are available for understanding them. I shall review what is known, and describe some analytic and numerical results.

The second half deals with a triply-periodic solutions (crystals) in a family of Skyrme systems, where the field takes values in the squashed 3-sphere. This family includes the standard Skyrme model (round 3-sphere) and the Faddeev-Hopf case (maximal squashing). In the round case, the lowest-energy crystal is a cubic lattice of half-skyrmions; but in the squashed case the crystal structure is different, and I shall describe some of the structures that arise.