Dbar-dressing method for the Gerdjikov–Ivanov equation with nonzero boundary conditions. (October 2021)

• Record Type: Journal Article
• Authors: Luo, Jinghua; Fan, Engui
• Is Part Of: Applied mathematics letters. Volume 120(2021)
• Publication Date: 2021-10
• Subjects: Gerdjikov–Ivanov equation -- Nonzero boundary condition -- Dbar-dressing method -- Lax pair -- Soliton solution; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107297
• Languages: English
• ISSNs: 0893-9659

Abstract

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.