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

The existence of Bogomolny decompositions for gauged baby Skyrme models