Dbar-dressing method for the Gerdjikov–Ivanov equation with nonzero boundary conditions. (October 2021) - Luo, Jinghua; Fan, Engui
Abstract: We apply the Dbar-dressing method to study a Gerdjikov–Ivanov (GI) equation with nonzero boundary at infinity. A spatial and a time spectral problem associated with GI equation are derived with a asymptotic expansion method. The N-soliton solutions of the GI equation are constructed based the Dbar-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. Highlights: The ∂ ̄ -dressing method to study the GI equation with nonzero boundary. A spatial and a time spectral problem associated with GI equation are derived. N-solitons of the GI equation with nonzero boundary are constructed.