Rogue-wave interaction for the Heisenberg ferromagnetism system

Heisenberg-type models for spin–spin interactions have been used to explain magnetic ordering in ferromagnetic materials. In this paper, a generalized, inhomogeneous, nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin system is investigated. By virtue of the generalized Darboux transformation, higher-order rogue-wave solutions are derived. Wave propagation and interaction are analyzed: (1) bright-rogue waves are found; (2) perturbation parametes and inhomogeneities in the medium of the system affect the direction and existing time of the first-order rogue-wave propagation; (3) perturbation parameters and inhomogeneities in the medium of the system affect the shapes, distances, patterns, and existing times of the second- and third-order rogue-wave interactions; (4) the direction of each second-order rogue wave remains unvaried after the interaction. (paper)