Multiple nonlinear wave solutions of a generalized Heisenberg ferromagnet model and their interactions

Under investigation in this paper is a generalized Heisenberg ferromagnet (HF) equation which is named the Zhanbota-IIA equation. It is one of the integrable generalizations of the HF equation that plays an important role in nonlinear magnetization dynamics. Through the establishment of the N-fold Darboux transformation, a series of solutions will be obtained, including multi-solitons, one- and two-breathers, first- and higher-order rogue waves. Dynamic behaviors of those solutions will be analyzed, including several structures of rogue waves such as fundamental structure, triangular structure, ring structure and ring-fundamental structure, the coexistence of rogue waves and breathers, i.e. semi-rational solution and the interaction of two breathers.