Solutions to the Master Equations Governing Fractional Vortices

Details Solutions to the Master Equations Governing Fractional Vortices Solutions to the Master Equations Governing Fractional Vortices

2012-04-12

arxiv.org/abs/1204.2818v1

Physics

Mathematical Physics

Scientific paper

By means of variational methods, in this paper, we establish sharp existence results for solutions of the master equations governing `fractional multiple vortices.' In the doubly periodic situation, the conditions for existence are both necessary and sufficient and give the upper bounds for the vortex numbers in terms of the size of the periodic cell domain. In the planar situation, there is no restriction on the vortex numbers. In both situations, the solutions are uniquely determined by the prescribed locations and the local winding numbers of the vortices.

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