The ∂¯-dressing method and Cauchy matrix for the defocusing matrix NLS system. (July 2021)

• Record Type: Journal Article
• Authors: Yao, Yuqin; Huang, Yehui; Fan, Engui
• Is Part Of: Applied mathematics letters. Volume 117(2021)
• Publication Date: 2021-07
• Subjects: ∂̄-dressing method -- Matrix NLS equation -- Lax pair -- Soliton solution; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107143
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The ∂ ̄ -dressing method is extended to study the matrix NLS equation. The defocusing matrix NLS equation is worked out based on a local 4 × 4 matrix ∂ ̄ -equation and two linear constraint equations. Explicit solutions, including N-soliton solutions are constructed by choosing a spectral transformation matrix and using the properties of the Cauchy matrix. Specially, the one-soliton solution, the superposition of two oppositely polarized displaced solitons and w-shaped soliton are obtained.