Geodesic
Adiabatic limit in the Ginzburg–Landau and Seiberg–Witten equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 233-242 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{TM_2010_270_a17,
     author = {A. G. Sergeev},
     title = {Adiabatic limit in the {Ginzburg{\textendash}Landau} and {Seiberg{\textendash}Witten} equations},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {233--242},
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     volume = {270},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a17/}
}
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A. G. Sergeev. Adiabatic limit in the Ginzburg–Landau and Seiberg–Witten equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 233-242. http://geodesic.mathdoc.fr/item/TM_2010_270_a17/

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