Periodic Cauchy problem of Heisenberg ferromagnet and its geometric framework.

We formulate algebraically solutions to the isotropic Heisenberg ferromagnet, which is an integrable geometric curve flow. The derivation is based on correspondences between this Heisenberg ferromagnet and the nonlinear Schrödinger equation. The existence of solutions to the Cauchy problems of the isotropic Heisenberg ferromagnet with periodic boundary conditions follows from the correspondence. We then obtain a geometric framework of algorithms to solve the periodic Cauchy problem numerically for the Heisenberg ferromagnet. Analytical and experimental results will be presented. [ABSTRACT FROM AUTHOR]