Multisolitons of the $U(N)$ generalized Heisenberg magnet model and the Yang–Baxter relation

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.