Dbar-dressing method for the Gerdjikov–Ivanov equation with nonzero boundary conditions

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-e...

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Bibliographic Details
Published in:Applied mathematics letters 2021-10, Vol.120, p.107297, Article 107297
Main Authors: Luo, Jinghua, Fan, Engui
Format: Article
Language:English
Subjects:
Dbar-dressing method
Gerdjikov–Ivanov equation
Lax pair
Nonzero boundary condition
Soliton solution
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Summary: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. •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.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2021.107297