By interchanging the roles of the space and time coordinates, we describe a
dual construction of the isotropic Landau-Lifshitz model, providing equal-space
Poisson brackets and dual Hamiltonians conserved with respect to
space-evolution. This construction is built in the Lax/zero-curvature
formalism, where the duality between the space and time dependencies is
evident.Comment: 18 Pages, LaTeX; Version accepted for publication in Physica D:
Nonlinear Phenomen
