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.
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