Integrability and solutions for a fourth-order lattice Gel'fand–Dikii equation. (January 2023) - Tela, Guesh Yfter; Zhang, Da-jun
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.