The Existence of Bogomolny Decompositions for Gauged $O(3)$ Nonlinear ``sigma'' Model and for Gauged Baby Skyrme Models

Abstract

The Bogomolny decompositions (Bogomolny equations) for the gauged baby Skyrme models: restricted and full one, in (2+0)-dimensions, are derived, for some general classes of the potentials. The conditions, which must be satisfied by the potentials, for each of these mentioned models, are also derived.