Geodesic
Generalized lattice Heisenberg magnet model and its quasideterminant soliton solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 197-208

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We consider a Darboux transformation of a generalized lattice (or semidiscrete) Heisenberg magnet (GLHM) model. We define a Darboux transformation on solutions of the Lax pair and on solutions of the spin evolution equation of the GLHM model. The solutions are expressed in terms of quasideterminants. We give a general expression for $K$-soliton solutions in terms of quasideterminants. Finally, we obtain one- and two-soliton solutions of the GLHM model using quasideterminant properties.
Keywords: discrete integrable system
Mots-clés : soliton, Darboux transformation. 
@article{TMF_2018_195_2_a2,
     author = {H. Wajahat A. Riaz and M. Hassan},
     title = {Generalized lattice {Heisenberg} magnet model and its quasideterminant soliton solutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--208},
     publisher = {mathdoc},
     volume = {195},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a2/}
}
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H. Wajahat A. Riaz; M. Hassan. Generalized lattice Heisenberg magnet model and its quasideterminant soliton solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 197-208. http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a2/