Geodesic
Algebraic-geometric solutions of the Dirac hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 563-574

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A Lenard equation is introduced, its two special solutions are given. One is used to derive an exceptional Dirac hierarchy, the other is applied to construct the generation function. The generation function yields conserved integrals of the Dirac Hamiltonian system, and defines an algebraic curve. Based on the theory of algebraic curve, the Dirac Hamiltonian system is proved to be integrable, the algebraic-geometric solutions of the Dirac hierarchy are obtained.
Keywords: Lenard equation; Dirac hierarchy; algebraic-geometric solution. 
@article{TMF_2017_193_3_a13,
     author = {Xiao Yang and Jiayan Han},
     title = {Algebraic-geometric solutions of the {Dirac} hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {193},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a13/}
}
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Xiao Yang; Jiayan Han. Algebraic-geometric solutions of the Dirac hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 563-574. http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a13/