  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.
