On the problem of classifying integrable chains with three independent variables

We discuss a new method for the classification of integrable nonlinear chains with three independent variables using an example of chains in the form . This method is based on reductions having the form of systems of differential–difference Darboux-integrable equations. It is well known that the cha...

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Bibliographic Details
Published inTheoretical and mathematical physics Vol. 215; no. 2; pp. 667 - 690
Main Authors Kuznetsova, M. N., Habibullin, I. T., Khakimova, A. R.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2023
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Applications of Mathematics
Classification
Differential equations
Independent variables
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Polynomials
Theoretical
Darboux integrability
three-dimensional chains
characteristic algebras
characteristic integrals
integrable reductions
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Summary:We discuss a new method for the classification of integrable nonlinear chains with three independent variables using an example of chains in the form . This method is based on reductions having the form of systems of differential–difference Darboux-integrable equations. It is well known that the characteristic algebras of Darboux-integrable systems have a finite dimension. The structure of the characteristic algebra is defined by some polynomial . The polynomial degree for the known integrable chains from the class under consideration equals or . A partial classification is performed in the case .
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577923050070