Breathers, rogue waves and semi-rational solutions for a Heisenberg ferromagnet-type equation

The Kuralay equation, as a Heisenberg ferromagnet-type equation, is of great significance for describing nonlinear phenomena in magnets. For the Kuralay-IIA equation, based on the constructed [Formula: see text]-fold Darboux transformation, we derive its one-fold and two-fold rogue wave solutions, one-breathers and two-breathers including the Akhmediev two-breathers. By adding shifts on the time variable, we further separate the Akhmediev two-breathers into two one-breathers. In addition, the semi-rational solutions consisting of the rogue wave and one-breather solutions are also derived. The diagrams of the obtained solutions are plotted to analyze their dynamic features.