Integrability and solutions for a fourth-order lattice Gel’fand–Dikii equation

Tela, Guesh Yfter; Zhang, Da‐jun

doi:10.1016/j.aml.2022.108424

Search citation statements

Order By: Relevance

Paper Sections

Select...

Conclusion and Remarks1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar feature holds for the GD-4 (A-2) equation, its alternative form and their four-component versions. Note that the MDC property has recently been used to construct Bäcklund transformation and find one-soliton solution to the GD-4 (B-2) equation, see [35]. Secondly, it is not clear how such GD-4 lattice equations are related to the discrete KP-type equations.…”

Section: Conclusion and Remarksmentioning

confidence: 99%

On the Fourth-Order Lattice Gel'fand-Dikii Equations

Tela¹,

Zhao²,

Zhang³

2023

SIGMA

View full text Add to dashboard Cite

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.

show abstract

Section: Conclusion and Remarksmentioning

confidence: 99%