Abstract
This paper investigates an integrable spin system (or Heisenberg ferromagnet-type equation or Nurshuak-IIA equation) which is an integrable generalization of the Heisenberg ferromagnet equation that raises from magneto-optical devices. The N-fold Darboux transformation of the Nurshuak-IIA equation will be constructed. With the selection of several parameters, a variety of the solutions will be produced, including breather–breather interactions, higher-order rogue waves and semi-rational solutions.
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