Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy

The methods of differential geometry are used to obtain a set of pseudopotential representations of the Landau–Lifshits equation that describes the nonlinear dynamics of a uniaxial ferromagnet. It is shown that linear pseudopotentials of a definite type are equivalent to a Lax representation. The direct scattering problem is investigated for some linear spectral problems associated with the Landau–Lifshits equation, and a polynomial series of conservation laws is found.