Abstract
We investigate the equations of motion in the four-dimensional non-anticommutative N=2 supersymmetric U(1) gauge field theory, in the search for BPS configurations. The BPS-like equations, generalizing the abelian (anti)self-duality conditions, are proposed. We prove full solvability of our BPS-like equations, as well their consistency with the equations of motion. Certain restrictions on the allowed scalar field values are also found. Surviving supersymmetry is briefly discussed too.
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