Self-dual compactons in the gauged restricted baby Skyrme model with magnetic impurity

Abstract: We investigate the existence of compact self-dual solitons in the restricted gauged baby Skyrme model in the presence of a magnetic impurity. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism depends on the relative size between the compacton and the impurity. To address this, we analyze the following scenarios: in the first, the impurity is entirely inside the compacton, and in the second, the impurity fully encircles the compacton. In both cases, the approach has enabled us to set the self-dual potential, achieve the Bogomol'ny bound for the energy, and establish the self-dual or BPS equations whose solutions saturate such a bound. We next focused on obtaining radially symmetric compactons, where for such an aim, we chose two types of functions to solve the BPS system: the first defining a step-type impurity and the second a Gaussian impurity. After solving the BPS system numerically, we depicted the resulting field profiles and highlighted the effects induced on the compacton's size, field profiles, magnetic field, and magnetic flux.