Geodesic
Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 371-381 
A. E. Borovik; V. N. Robuk. Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 371-381. http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a10/
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     title = {Linear pseudopotentials and conservation laws for the {Landau{\textendash}Lifshits} equation describing the nonlinear dynamics of a~ferromagnet with uniaxial anisotropy},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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