METHODS FOR STUDYING 3+1 LOCALIZED STRUCTURES - THE SKYRMION AS THE ABSOLUTE MINIMIZER OF ENERGY

General methods in search of stable structures in (3 + 1)-dimensional models are presented. Using the Skyrme model as an example, we exhibit the methods and demonstrate their ability to pick out the minimal-energy configurations. In the class of fields with unit topological charge these are the well-known Skyrmions (the spherically symmetric configurations), which realize the absolute minimum of the energy. In the second and higher homotopy classes the minimal-energy configurations are, however, of the axisymmetric type. We argue that these methods provide a good guide and support to numerical analysis of multidimensional structures in essentially nonlinear models for liquid crystals, cosmology, ferromagnets, nonlinear elasticity, and so on.