The negative flow Gerdjikov–Ivanov equation: Darboux transformation and breather solutions

Abstract Under investigation in this paper is the negative flow Gerdjikov–Ivanov (GI) equation. Based on the gauge transformation for a 2×2 matrix spectral problem, the general Darboux transformation for the unreduced coupled form of this equation is constructed and rigorously proven. Subsequently, the N -fold Darboux transformation for the negative flow GI equation is derived via a reduction technique. As an application, the N -breather solution under the plane-wave background is obtained. Particularly, explicit solutions including the one-, two- and three-breather solutions are presented and shown graphically.