Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps. (7th May 2021)

• Record Type: Journal Article
• Authors: Xu, Xiaoxue; Cao, Cewen; Nijhoff, Frank W
• Is Part Of: Nonlinearity. Volume 34:Number 5(2021)
• Page Start: 2897
• Page End: 2918
• Publication Date: 2021-05-07
• Subjects: Baker–Akhiezer functions -- algebro-geometric solutions -- integrable lattice equations -- integrable symplectic maps; 37J10 -- 37K10 -- 39A14; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abddca
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: The Q1 lattice equation, a member in the Adler–Bobenko–Suris list of 3D consistent lattices, is investigated. By using the multidimensional consistency, a novel Lax pair for Q1 equation is given, which can be nonlinearized to produce integrable symplectic maps. Consequently, a Riemann theta function expression for the discrete potential is derived with the help of the Baker–Akhiezer functions. This expression leads to the algebro-geometric integration of the Q1 lattice equation, based on the commutativity of discrete phase flows generated from the iteration of integrable symplectic maps.