Geodesic
Adiabatic limit in the Ginzburg--Landau and Seiberg--Witten equations
Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 233-242.

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We study an adiabatic limit in $(2+1)$-dimensional hyperbolic Ginzburg–Landau equations and 4-dimensional symplectic Seiberg–Witten equations. In dimension $3=2+1$ the limiting procedure establishes a correspondence between solutions of Ginzburg–Landau equations and adiabatic paths in the moduli space of static solutions, called vortices. The 4-dimensional adiabatic limit may be considered as a complexification of the $(2+1)$-dimensional procedure with time variable being “complexified.” The adiabatic limit in dimension $4=2+2$ establishes a correspondence between solutions of Seiberg–Witten equations and pseudoholomorphic paths in the moduli space of vortices. 
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     author = {A. G. Sergeev},
     title = {Adiabatic limit in the {Ginzburg--Landau} and {Seiberg--Witten} equations},
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     volume = {270},
     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a17/}
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A. G. Sergeev. Adiabatic limit in the Ginzburg--Landau and Seiberg--Witten equations. Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 233-242. http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a17/

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