Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model

Details Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model

2006-11-02

arxiv.org/abs/nlin/0611002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, 5 figures

Scientific paper

The problem of magnetic vortex dynamics in an anisotropic spin liquid model is considered. For incompressible flow the model admits reduction to saturating Bogomolny inequality analytic projections of spin variables, subject the linear holomorphic Schr\"odinger equation. It allows us to construct N vortex configurations in terms of the complex Hermite polynomials. Using complex Galilean boost transformations, the interaction of the vortices and the vortex chain lattices (vortex crystals) are studied. By the complexified Cole-Hopf transformation, integrable N vortex dynamics is described by the holomorphic Burgers equation. Mapping of the point vortex problem to N-particle problem, the complexified Calogero-Moser system, showing its integrability and the Hamiltonian structure, is given.

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