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

The integrable higher-order Heisenberg spin system with quintic terms in self-consistent potential (HHSQ) is an extension of Heisenberg ferromagnetic equations. In this paper, we calculate the Lax expression of the HHSQ system, then the motioning curves in [Formula: see text] dimension of Heisenberg ferromagnetic equations have been discussed. The Darboux transformation of the HHSQ system is constructed and a set of soliton solutions will be demonstrated by Darboux transformation.