[كتاب][B] Continuous symmetries and integrability of discrete equations

D Levi, P Winternitz, RI Yamilov - 2023‏ - books.google.com
This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

Multi-component extension of CAC systems

DD Zhang, PH Van der Kamp, DJ Zhang - SIGMA. Symmetry, Integrability …, 2020‏ - emis.de
In this paper an approach to generate multi-dimensionally consistent $ N $-component
systems is proposed. The approach starts from scalar multi-dimensionally consistent …

Classification of a subclass of two-dimensional lattices via characteristic Lie rings

I Habibullin, M Poptsova - SIGMA. Symmetry, Integrability and Geometry …, 2017‏ - emis.de
The main goal of the article is testing a new classification algorithm. To this end we apply it
to a relevant problem of describing the integrable cases of a subclass of two-dimensional …

A classification algorithm for integrable two-dimensional lattices via Lie—Rinehart algebras

IT Habibullin, MN Kuznetsova - Theoretical and Mathematical Physics, 2020‏ - Springer
We study the problem of the integrable classification of nonlinear lattices depending on one
discrete and two continuous variables. By integrability, we mean the presence of reductions …

[PDF][PDF] Algebraic entropy for systems of quad equations

G Gubbiotti - Open Communications in Nonlinear …, 2024‏ - ocnmp.episciences.org
In this work I discuss briefly the calculation of the algebraic entropy for systems of quad
equations. In particular, I observe that since systems of multilinear equations can have …

Integrability conditions for two-dimensional Toda-like equations

IT Habibullin, MN Kuznetsova… - Journal of Physics A …, 2020‏ - iopscience.iop.org
In the article some algebraic properties of nonlinear two-dimensional lattices of the form un,
xy= f (u n+ 1, un, un− 1) are studied. The problem of exhaustive description of the integrable …

Darboux integrability of trapezoidal H4 and H4 families of lattice equations I: first integrals

G Gubbiotti, RI Yamilov - Journal of Physics A: Mathematical and …, 2017‏ - iopscience.iop.org
In this paper we prove that the trapezoidal H4 and the H6 families of quadequations are
Darboux integrable by constructing their first integrals. This result explains why the rate of …

Integrability of difference equations through algebraic entropy and generalized symmetries

G Gubbiotti - Symmetries and Integrability of Difference Equations …, 2017‏ - Springer
Given an equation arising from some application or theoretical consideration one of the first
questions one might ask is: What is its behavior? It is integrable? In these lectures we will …

Difference systems in bond and face variables and non-potential versions of discrete integrable systems

P Kassotakis, M Nieszporski - Journal of Physics A: Mathematical …, 2018‏ - iopscience.iop.org
Integrable discrete scalar equations defined on a 2D or 3D lattice can be rewritten as
difference systems in bond variables or in face variables, respectively. Both the difference …

О классификационном алгоритме интегрируемых двумеризованных цепочек на основе алгебр Ли–Райнхарта

ИТ Хабибуллин, МН Кузнецова - Теоретическая и математическая …, 2020‏ - mathnet.ru
Исследуется задача интегрируемой классификации нелинейных цепочек, зависящих
от одной дискретной и двух непрерывных переменных. Под интегрируемостью …