Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory

We consider the adiabatic limit for nonlinear dynamic equations of gauge field theory. Our main example of such equations is given by the Abelian $(2+1)$-dimensional Higgs model. We show next that the Taubes correspondence, which assigns pseudoholomorphic curves to solutions of Seiberg–Witten equations on symplectic 4-manifolds, may be interpreted as a complex analogue of the adiabatic limit construction in the $(2+1)$-dimensional case.