Self-dual compactons in the gauged restricted baby Skyrme model in the presence of an external magnetic field
We investigate the existence of compact self-dual solitons in the restricted gauged baby Skyrme model in the presence of an external magnetic field. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism depends on the relative size between the compacton and the effective region occupied by the external magnetic field. To address this issue, we consider two scenarios: in the first, the external magnetic field is confined within the compacton, effectively playing the role of a magnetic impurity; in the second scenario, the external magnetic field fully encircles the compacton. For 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 by solving the BPS system using two functions to describe the external magnetic field, a step-type function and a Gaussian function. 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.