Inverse Scattering Transform for the Focusing Ablowitz‐Ladik System with Nonzero Boundary Conditions. Issue 1 (30th November 2015)

• Record Type: Journal Article
• Authors: Prinari, Barbara; Vitale, Federica
• Other Names: Biondini G. guestEditor.; Fokas A.S. guestEditor.
• Is Part Of: Studies in applied mathematics. Volume 137:Issue 1(2016)
• Page Start: 28
• Page End: 52
• Publication Date: 2015-11-30
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12103
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract : The purpose of this paper is to construct the inverse scattering transform for the focusing Ablowitz‐Ladik equation with nonzero boundary conditions at infinity. Both the direct and the inverse problems are formulated in terms of a suitable uniform variable; the inverse problem is posed as a Riemann‐Hilbert problem on a doubly connected curve in the complex plane, and solved by properly accounting for the asymptotic dependence of eigenfunctions and scattering data on the Ablowitz‐Ladik potential.