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We construct entire solutions of the magnetic Ginzburg-Landau equations indimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutionsare close to the minimal submanifolds studied by Arezzo-Pacard\cite{Arezzo}. Wealso show the existence of a saddle type solution to the equations, whose zeroset consists of two vertical planes in $\mathbb{R}^4$. These two types ofsolutions are believed to be energy minimizers of the corresponding energyfunctional and lie in the same connect component of the moduli space of entiresolutions.

Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$