Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations. Issue 1 (13th November 2020)

• Record Type: Journal Article
• Authors: Xu, Xiaoxue; Jiang, Mengmeng; Nijhoff, Frank W
• Is Part Of: Studies in applied mathematics. Volume 146:Issue 1(2021)
• Page Start: 233
• Page End: 278
• Publication Date: 2020-11-13
• Subjects: Baker‐Akhiezer functions -- discrete Korteweg‐de Vries‐type equations -- finite genus solutions -- integrable Hamiltonian systems -- integrable symplectic maps; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12346
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: In this paper, we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable partial difference equations which are the discrete counterparts of integrable partial differential equations of Korteweg‐de Vries‐type (KdV‐type). As a consequence it is demonstrated that several distinct Hamiltonian systems lead to one and the same difference equation by means of the Liouville integrability framework. Thus, these integrable symplectic maps may provide an efficient tool for characterizing, and determining the integrability of, partial difference equations.