Bianchi Permutability for the Anti‐Self‐Dual Yang‐Mills Equations. Issue 1 (16th February 2016)

• Record Type: Journal Article
• Authors: Benincasa, Gregorio B.; Halburd, Rod
• Other Names: Biondini G. guestEditor.; Fokas A.S. guestEditor.
• Is Part Of: Studies in applied mathematics. Volume 137:Issue 1(2016)
• Page Start: 110
• Page End: 122
• Publication Date: 2016-02-16
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12118
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract : The anti‐self‐dual Yang‐Mills equations are known to have reductions to many integrable differential equations. A general Bäcklund transformation (BT) for the anti‐self‐dual Yang‐Mills (ASDYM) equations generated by a Darboux matrix with an affine dependence on the spectral parameter is obtained, together with its Bianchi permutability equation. We give examples in which we obtain BTs of symmetry reductions of the ASDYM equations by reducing this ASDYM BT. Some discrete integrable systems are obtained directly from reductions of the ASDYM Bianchi system.