Integrability and solutions for a fourth-order lattice Gel'fand–Dikii equation. (January 2023)

• Record Type: Journal Article
• Authors: Tela, Guesh Yfter; Zhang, Da-jun
• Is Part Of: Applied mathematics letters. Volume 135(2023)
• Publication Date: 2023-01
• Subjects: Multidimensional consistency -- Bäcklund transformation -- Soliton solution -- Fourth-order lattice Gel'fand–Dikii equation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108424
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this letter, we investigate a lattice fourth-order Gel'fand–Dikii quadrilateral system. It is an extension of Hietarinta's (B-2) equation of the discrete Boussinesq type. We show that the system is multidimensionally consistent, which determines its discrete integrability and gives rise to a Bäcklund transformation. A seed solution and a one-soliton solution are derived using the Bäcklund transformation. The plane wave factor in the one-soliton solution indicates this system is related to a quartic polynomial, which characterizes discrete dispersion relations. Dynamics and asymptotic behaviors are illustrated.