Geodesic
Nonlocal matrix hamiltonian operators, differential geometry, and applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 452-462

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A study is made of a class of nonlocal Hamiltonian operators that arise naturally as second Hamittonian structures of the nonlinear Schrödinger equation, the Heisenberg magnet, the Landau–Lifshitz equation, etc. A complete description of these operators is obtained, and it reveals intimate connections with classical differential geometry. A new nonlocal Hamiltonian structure of first order is constructed for the partly anisotropic ($J_1=J_2$) Landau–Lifshitz equation (hitherto, only Hamiltonian structures of zeroth and second orders were known for the Landau–Lifshitz equation). 
@article{TMF_1992_91_3_a9,
     author = {E. V. Ferapontov},
     title = {Nonlocal matrix hamiltonian operators, differential geometry, and applications},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {452--462},
     publisher = {mathdoc},
     volume = {91},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a9/}
}
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E. V. Ferapontov. Nonlocal matrix hamiltonian operators, differential geometry, and applications. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 452-462. http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a9/