Integrability of auto-Bäcklund transformations and solutions of a torqued ABS equation. (4th June 2021)

• Record Type: Journal Article
• Authors: Wei, Xueli; van der Kamp, Peter H; Zhang, Da-jun
• Is Part Of: Communications in theoretical physics. Volume 73:Number 7(2021)
• Publication Date: 2021-06-04
• Subjects: auto-Bäcklund transformation -- consistency -- Lax pair -- soliton solution -- torqued ABS equation -- semi-autonomous; Physics -- Periodicals; 530.105
• DOI: 10.1088/1572-9494/abfcba
• Languages: English
• ISSNs: 0253-6102

Abstract

Abstract: An auto-Bäcklund transformation for the quad equation Q11 is considered as a discrete equation, called H2 a, which is a so called torqued version of H2. The equations H2 a and Q11 compose a consistent cube, from which an auto-Bäcklund transformation and a Lax pair for H2 a are obtained. More generally it is shown that auto-Bäcklund transformations admit auto-Bäcklund transformations. Using the auto-Bäcklund transformation for H2 a we derive a seed solution and a one-soliton solution. From this solution it is seen that H2 a is a semi-autonomous lattice equation, as the spacing parameter q depends on m but it disappears from the plane wave factor.