Application of the Riemann–Hilbert approach to the multicomponent AKNS integrable hierarchies. (June 2019)

• Record Type: Journal Article
• Authors: Ma, Wen-Xiu
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 1
• Page End: 17
• Publication Date: 2019-06
• Subjects: Integrable hierarchy -- Riemann–Hilbert problem -- Soliton solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.09.017
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A class of Riemann–Hilbert problems on the real axis is formulated for solving the multicomponent AKNS integrable hierarchies associated with a kind of bock matrix spectral problems. Through special Riemann–Hilbert problems where a jump matrix is taken to be the identity matrix, soliton solutions to all integrable equations in each hierarchy are explicitly computed. A class of specific reductions of the presented integrable hierarchies is also made, together with its reduced Lax pairs and soliton solutions.