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Nonlocal matrix hamiltonian operators, differential geometry, and applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 452-462 Cet article a éte moissonné depuis la source Math-Net.Ru

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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). 
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     author = {E. V. Ferapontov},
     title = {Nonlocal matrix hamiltonian operators, differential geometry, and applications},
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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/

[1] Dubrovin B. A., Novikov S. P., DAN SSSR, 270:4 (1983), 781–785 | MR | Zbl

[2] Mokhov O. I., Ferapontov E. V., UMN, 45:3 (1990), 191–192 | MR | Zbl

[3] Oevel G., Fuchsteiner B., Blaszak M., Progr. Theor. Phys., 83:3 (1990), 395–413 | DOI | MR | Zbl

[4] Sidorenko Yu. H., “Voprosy kvantovoi teorii polya i statisticheskoi fiziki”, Zapiski nauchnykh seminarov LOMI, 161, no. 7, 1987, 76–87

[5] Gerdjikov V. S., Yanovski A. B., Commun. Math. Phys., 103:4 (1986), 549–568 | DOI | MR | Zbl

[6] Barouch E., Fokas A. S., Papageorgiou V. G., J. Math. Phys., 29:12 (1988), 2628–2633 | DOI | MR | Zbl

[7] van Bemmelen T., Kersten P., J. Math. Phys., 32:7 (1991), 1709–1716 | DOI | MR | Zbl

[8] Ferapontov E. V., Problemy geometrii, 22, VINITI, M., 1990, 59–96 | MR

[9] Ferapontov E. V., Funkts. analiz i ego prilozh., 25:3 (1991), 37–49 | MR | Zbl