  Using recently proposed non-linearly realized supersymmetry in non-Abelian
gauge theory corrected to the order (alpha')^2, we derive the non-linear BPS
equations in the background B-field for the U(2) monopoles and instantons. We
show that these non-Abelian non-linear BPS equations coincide with the
non-commutative anti-self-dual equations via the Seiberg-Witten map.
