On the Fourth-Order Lattice Gel'fand-Dikii Equations
Exactly Solvable and Integrable Systems
2023-02-22 v2
Abstract
The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lattice Gel'fand-Dikii type. These equations are related to a quartic discrete dispersion relation and can be viewed as higher-order members of the extended lattice Boussinesq type equations. The resulting lattice equations given here are in five-component form, and some of them are multi-dimensionally consistent by introducing extra equations. Lax integrability is discussed both by direct linearization scheme and also through multi-dimensional consistent property. Some reductions of the five-component lattice equations to the four-component forms are considered.
Keywords
Cite
@article{arxiv.2206.14403,
title = {On the Fourth-Order Lattice Gel'fand-Dikii Equations},
author = {Guesh Yfter Tela and Song-Lin Zhao and Da-Jun Zhang},
journal= {arXiv preprint arXiv:2206.14403},
year = {2023}
}