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This article is cited in 1 scientific paper (total in 1 paper)
On the Fourth-Order Lattice Gel'fand–Dikii Equations
Guesh Yfer Telaa, Song-Lin Zhaob, Da-Jun Zhanga a Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
b Department of Applied Mathematics, Zhejiang University of Technology,
Hangzhou 310023, P.R. China
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:
lattice Gel'fand–Dikii type equation, direct linearization approach, multi-dimensional consistency, Lax pair.
Received: July 2, 2022; in final form February 6, 2023; Published online February 21, 2023
Citation:
Guesh Yfer Tela, Song-Lin Zhao, Da-Jun Zhang, “On the Fourth-Order Lattice Gel'fand–Dikii Equations”, SIGMA, 19 (2023), 007, 30 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1902 https://www.mathnet.ru/eng/sigma/v19/p7
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