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تسجيل مستخدم جديدEntire solutions of the magnetic Ginzburg-Landau equation in $mathbb{R}^4$
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We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacardcite{Arezzo}. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in $mathbb{R}^4$. These two types of solutions are believed to be energy minimizers of the corresponding energy functional and lie in the same connect component of the moduli space of entire solutions.
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