Geodesic
Multicomponent generalization of the hierarchy of the Landau--Lifshitz equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 62-71

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We construct a second-order $2N$-component integrable system (with arbitrary $N$) whose spectral parameter lies on a curve of genus $g=1+(N-3)2^{N-2}$. The odd-order flows admit $N$-component reductions, which for $N=3$ coincide with the odd-order flows of the hierarchy of the Landau–Lifshitz equation. 
@article{TMF_2000_124_1_a4,
     author = {I. Z. Golubchik and V. V. Sokolov},
     title = {Multicomponent generalization of the hierarchy of the {Landau--Lifshitz} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {62--71},
     publisher = {mathdoc},
     volume = {124},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a4/}
}
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I. Z. Golubchik; V. V. Sokolov. Multicomponent generalization of the hierarchy of the Landau--Lifshitz equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 62-71. http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a4/