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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 2, Pages 208–221
DOI: https://doi.org/10.4213/tmf9890 (Mi tmf9890) 		 
Multisolitons of the $U(N)$ generalized Heisenberg magnet model and the Yang–Baxter relation

Z. Amjad, B. Haider

Department of Physics, University of the Punjab, Lahore, Pakistan
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DOI: https://doi.org/10.4213/tmf9890
Abstract: 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, $r$-matrix, conserved quantity.
Received: 19.02.2020
Revised: 21.06.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 2, Pages 1426–1438
DOI: https://doi.org/10.1134/S0040577920110033
Bibliographic databases:
Document Type: Article
PACS: 11.30.Pb, 11.10.Nx, 04.20.Jb, 02.30.Ik
Language: Russian
Citation: Z. Amjad, B. Haider, “Multisolitons of the $U(N)$ generalized Heisenberg magnet model and the Yang–Baxter relation”, TMF, 205:2 (2020), 208–221; Theoret. and Math. Phys., 205:2 (2020), 1426–1438
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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