Breathers and rogue waves of the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

Abstract

One-dimensional anisotropic Heisenberg ferromagnetic spin chain can be described by the fifth-order nonlinear Schrodinger equation, which is investigated in this paper. Through the Darboux transformation, we obtain the Akhmediev breathers (ABs), Kuznetsov–Ma (KM) solitons and rogue-wave solutions. Effects of the coefficients of the fourth-order dispersion, $$\gamma $$ , and of the fifth-order dispersion, $$\delta $$ , on the properties of ABs, KM solitons and rogue waves are discussed: (1) With $$\gamma $$ increasing, the AB exhibits stronger localization in time; (2) The propagation directions of an AB and a KM soliton change with the presence of $$\delta $$ ; and (3) Enhancement of $$\gamma $$ makes the existence time of the rogue waves shorter, while enhancement of $$\delta $$ increases the existence time of the rogue waves.