On the Higher-order Heisenberg spin chain system with quintic terms in self-consistent potential

In this paper, a Higher-order Heisenberg spin chain system with quintic terms in selfconsistent potential is investigated, which is one of a generalization of the Heisenberg ferromagnetic equations and is integrable. We firstly obtain the Lax representation of the Higher-order Heisenberg spin chain system with quintic terms in self-consistent potential. Secondly, we discuss integrable Heisenberg ferromagnetic equations motioning curves in (1+1) dimension. Further, the Darboux transformation of the Heisenberg spin chain system with quintic terms in self-consistent potential is constructed, and we discuss a soliton solution by Darboux transformation.