On Decomposition of the ABS Lattice Equations and Related Bäcklund Transformations. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Zhang, Danda; Zhang, Da-jun
• Is Part Of: Journal of nonlinear mathematical physics. Volume 25:Issue 1(2018)
• Page Start: 34
• Page End: 53
• Publication Date: 2018-01-02
• Subjects: ABS list -- decomposition -- Bäcklund transformation -- solutions -- weak Lax pair; 35Q51 -- 35Q55 -- 37K05 -- 39A99; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2018.1440741
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : The Adler-Bobenko-Suris (ABS) list contains scalar quadrilateral equations which are consistent around the cube, and have D 4 symmetry and tetrahedron property. Each equation in the ABS list admits a beautiful decomposition. We revisit these decomposition formulas and by means of them we construct Bäcklund transformations (BTs). BTs are used to construct lattice equations, their new solutions and weak Lax pairs.