2021/02/15 by I. T. Habibullin, A R Khakimova, A. R. Khakimova
Biochemistry, Genetics and Molecular Biology · Mathematics · Pharmacology, Toxicology and Pharmaceutics · Physics and Astronomy · #Algebra over a field #Algebraic number #Biological Activity of Diterpenoids and Biflavonoids #Class (philosophy) #Computer science #Curse of dimensionality #Differential equation #Field (mathematics) #Integrable system #Lie algebra #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Plant-based Medicinal Research #Property (philosophy) #Pure mathematics #Vector field #nlin.SI
paper · pdf · doi:10.1088/1751-8121/ac070c
24 pages
arxiv created 2021/02/15 · openalex publication_date 2021/06/01 · arxiv updated 2021/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract The purpose of this article is to discuss an algebraic method for studying integrable differential-difference lattices with two discrete and one continuous independent variables. The main idea is based on the hypothesis that any integrable equation of this type admits an infinite sequence of reductions, which are Darboux integrable systems of differential-difference equations with two independent variables. To detect the Darboux integrability property of the reductions the authors use the characteristic Lie–Rinehart algebras. The hypothesis is confirmed by integrable three-dimensional lattices from the list given by Ferapontov et al (2015 Int. Math. Res. Not. 2015 4933). The required reductions are found for these lattices. Characteristic algebras corresponding to small-order reductions are described, integrals are calculated in both directions, which proves Darboux integrability. The approach might be useful for the integrable classification in 3D.