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

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.