Abstract
In this paper, for the Kaup–Newell (KN) system, by making use of the determinant representations of n-fold Darboux transformation (DT) and n-transformed solutions, we obtain similar conclusions for the fourth-order flow equation of the KN system (FOFEKN). Furthermore, on one hand, starting from the zero seed solution q=0, we obtain several exact solutions of the reduced FOFEKN, such as soliton solutions and positon solutions. On the other hand, if we start with the periodic non-zero seed solution, then we obtain some breather solutions and rogue wave solutions of the reduced FOFEKN.
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