Characteristics of rogue waves for a (2+1)-dimensional Heisenberg ferromagnetic spin chain system

A (2 + 1)-dimensional equation is investigated, which describes a Heisenberg ferromagnetic spin chain system in ferrite material. Through using Hirota bilinear method and choosing proper polynomial functions in bilinear forms, the one-order rogue waves solution and its existence condition are obtained. Based on this existence condition, the two-order rouge waves solution is also obtained. Furthermore, some interesting characteristics of the rogue waves are observed by visualization method. For the one-order rogue waves, there exist three types of single-, two- and three-petal states. For the two-order rogue waves, there are six types in term of the arrangement of bright peaks. The impacts of system parameters on the rogue waves are also discussed. These results are new for the Heisenberg ferromagnetic spin chain system.