Groebli solution for three magnetic vortices

S. Komineas; N. Papanicolaou

doi:10.1063/1.3393506

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arXiv · 0911.2377

Groebli solution for three magnetic vortices

S. Komineas·N. Papanicolaou

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Abstract

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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S. Komineas, N. Papanicolaou. 2009-11-12. Groebli solution for three magnetic vortices. https://doi.org/10.1063/1.3393506

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