We formulate algebraically solutions to the isotropic Heisen- berg ferromagnet, which is an integrable geometric curve flow. The derivation is based on correspondences between this Heisenberg ferromagnet and the nonlinear Schro ̈dinger 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.
Journal of Fixed Point Theory and Applications 24, 16