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Variational approach to uniform rigid rotation of Ginzburg-Landau vortices. (English) Zbl 0979.58006

The main result of the paper establishes the existence of time-periodic solutions to the second-order time-dependent equation associated to the Ginzburg-Landau action, with the additional property that the solution at a fixed time is a nontrivial rigid rotation of the initial data. The authors use a direct variational approach obtaining the solutions as critical points of a suitable indefinite functional. Physical interpretations are also discussed.

MSC:

58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
35Q99 Partial differential equations of mathematical physics and other areas of application
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