ON A SPECIAL COUPLED LATTICE SYSTEM OF THE DISCRETE BOUSSINESQ TYPE. Issue 2 (April 2023)

• Record Type: Journal Article
• Authors: Yfter Tela, Guesh; Zhang, Da-jun
• Is Part Of: Reports on mathematical physics. Volume 91:Issue 2(2023)
• Page Start: 219
• Page End: 235
• Publication Date: 2023-04
• Subjects: Bäcklund transformation -- bilinear form -- soliton -- discrete Boussinesq family -- consistency-around-cube; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(23)00026-5
• Languages: English
• ISSNs: 0034-4877

Abstract

Abstract : In this paper, we investigate a multidimensionally consistent coupled quadrilateral system of the discrete Boussinesq type, proposed by Fordy and Xenitidis recently. It is distinguished from the known discrete Boussinesq type equations by a special dispersion relation. A Bäcklund transformation is constructed and a one-soliton solution is derived using the Bäcklund transformation. We also give bilinear forms of the coupled equations and present formulae for multisoliton solutions. Both plane wave factor and phase factor in two-soliton solutions indicate the coupled systems belong to the discrete Boussinesq family, but there is no continuous correspondence in terms of the Miwa coordinates.