Paper detail

Integrable motion of anisotropic space curves and surfaces induced by the Landau-Lifshitz equation

In this paper, we have studied the geometrical formulation of the Landau-Lifshitz equation (LLE) and established its geometrical equivalent counterpart as some generalized nonlinear Schrödinger equation. When the anisotropy vanishes, from this result follows the well-known results corresponding for the isotropic case, i.e. to the Heisenberg ferromagnet equation and the focusing nonlinear Schrödinger equation. The relations between the LLE and the differential geometry of space curves in the local and nonlocal cases are studied. Using the well-known Sym-Tafel formula, the soliton surfaces induced by the LLE are briefly considered.