∂̄-dressing method for the (2+1)-dimensional Korteweg–de Vries equation. (June 2023)

• Record Type: Journal Article
• Authors: Yang, Shuxin; Li, Biao
• Is Part Of: Applied mathematics letters. Volume 140(2023)
• Publication Date: 2023-06
• Subjects: ∂̄-dressing method -- Green's function -- Characteristic function -- (2+1)-dimensional kdV equation -- Inverse spectral transformation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2023.108589
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we investigate the (2+1)-dimensional Korteweg–de Vries equation by applying the ∂ ̄ -dressing method. A new ∂ ̄ problem is obtained through the characteristic functions and Green's functions by Lax representation. A solution of ∂ ̄ problem is constructed by applying Cauchy–Green formula and selecting appropriate spectral transformation. Finally, we can give the solution of the (2+1) dimensional Korteweg–de Vries equation after determining the time evolution of the spectral data.