∂̄-dressing method for the coupled Gerdjikov–Ivanov equation. (December 2020) - Luo, Jinghua; Fan, Engui
Abstract: We apply the ∂ ̄ -dressing method to study a coupled Gerdjikov–Ivanov (GI) equation. Compared with results on the classical coupled GI equation, more general spatial and a time singular spectral problems associated with GI equation are derived from a local 2 × 2 matrix ∂ ̄ -equation via two linear constraint equations. A more general GI hierarchy with source is proposed by using recursive operator. The N -solitons of the coupled GI equation are constructed still based the ∂ ̄ -equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. The results on the GI equation can be recovered from the conclusion given above as special reductions.