Work

On trilinear and quadrilinear equations associated with the lattice Gel’fand–Dikii hierarchy

Year: 2024

Type: article

Abstract: Introduced in Zhang et al. (2012), the trilinear Boussinesq equation is the natural form of the equation for the τ -function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontrivial derivation from the bilinear lattice AKP equation under dimensional reduction, a quadrilinear dual lattice equation, conservation laws, and periodic reductions leading to higher-dimensional integrable maps and their Laurent property. Furthermore, we consider a higher Gel’fand–Dikii lattice system, its periodic reductions and Laurent property. As a special application, from both a trilinear Boussinesq recurrence as well as a higher Gel’fand–Dikii system of three bilinear recurrences, we establish Somos-like integer sequences.

Source: Partial Differential Equations in Applied Mathematics

DOI: 10.1016/j.padiff.2024.100913

Authors: P.H. van der Kamp, F.W. Nijhoff, D.I. McLaren, G.R.W. Quispel

Institutions: University of Leeds, La Trobe University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,230

Funder: Engineering and Physical Sciences Research Council