There are Asymmetric Minimizers for the One-Dimensional Ginzburg-Landau Model of Superconductivity
S. P. Hastings, W. C. Troy
Abstract
We study a boundary value problem associated with a system of two second order differential equations with cubic nonlinearity which model a film of superconductor material subjected to a tangential magnetic field. We show that for an appropriate range of parameters there are asymmetric solutions, and only trivial symmetric solutions. We then show that the associated energy function is negative for the asymmetric solutions, and zero for the trivial symmetric solution. It follows that a global minimizer of the energy is asymmetric.
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