ON TOPOLOGICAL SOLITON DYNAMICS IN MULTIDIMENSIONAL FERROMAGNETIC CONTINUUM

A multidimensional model for a ferromagnetic continuum with hydrodynam ical properties, which can be regarded as a modified Landau-Lifshitz e quation, is presented. The treatment of some physical examples suggest s that the fluid vorticity has to be proportional to the magnetic topo logical current. The model can be written in the Hirota bilinear form. In two spatial dimensions, the existence of a positive definite 'ener gy' functional is shown. The Bogomol'nyi inequality leads to the self- dual equations of the model, which can be expressed by the Liouville e quation: By using time-dependent gauge transformations, a wide class o f solutions can be generated. These are, in general, associated with t he linear problem of the modified Kadomtsev-Petviashvili equation: In some particular cases, the isolated vortices can move along arbitrary trajectories on the plane. The quantization problem of the time-depend ent vortex configurations is briefly discussed, is relation to the pos sible evaluation of their energy spectrum.