Geodesic
Multisolitons of the~$U(N)$ generalized Heisenberg magnet model and the~Yang--Baxter relation
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 208-221

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We use the binary Darboux transformation to obtain exact multisoliton solutions of the $U(N)$ generalized Heisenberg magnet model and present the solutions in terms of quasideterminants. In addition, based on using the Poisson bracket algebra, we develop a new canonical approach of the type of the $r$-matrix approach for the generalized Heisenberg magnet model.
Keywords: quasideterminant, noncommutative integrable system, binary Darboux transformation, conserved quantity.
Mots-clés : $r$-matrix 
@article{TMF_2020_205_2_a2,
     author = {Z. Amjad and B. Haider},
     title = {Multisolitons of the~$U(N)$ generalized {Heisenberg} magnet model and {the~Yang--Baxter} relation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {208--221},
     publisher = {mathdoc},
     volume = {205},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a2/}
}
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Z. Amjad; B. Haider. Multisolitons of the~$U(N)$ generalized Heisenberg magnet model and the~Yang--Baxter relation. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 208-221. http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a2/