Groebli solution for three magnetic vortices

Details Groebli solution for three magnetic vortices Groebli solution for three magnetic vortices

2009-11-12

arxiv.org/abs/0911.2377v1

J. Math. Phys. 51, 042705 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

19 pages, 6 figures

Scientific paper

10.1063/1.3393506

The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable Hamiltonian system for N=2 or 3 but chaotic dynamics for N>3. Here we consider a generalization of the HK equations to describe the dynamics of magnetic vortices within a collective-coordinate approximation. In particular, we analyze in detail the dynamics of a system of three magnetic vortices by a suitable generalization of the solution for three point vortices in an ordinary fluid obtained by Groebli more than a century ago. The significance of our results for the dynamics of ferromagnetic elements is briefly discussed.

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