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

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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. 
@article{TMF_1981_46_3_a10,
     author = {A. E. Borovik and V. N. Robuk},
     title = {Linear pseudopotentials and conservation laws for the {Landau--Lifshits} equation describing the nonlinear dynamics of a~ferromagnet with uniaxial anisotropy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {371--381},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a10/}
}
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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/