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[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 …
symmetries and integrability techniques to the case of equations defined on the lattice. This …
Multi-component extension of CAC systems
In this paper an approach to generate multi-dimensionally consistent $ N $-component
systems is proposed. The approach starts from scalar multi-dimensionally consistent …
systems is proposed. The approach starts from scalar multi-dimensionally consistent …
Classification of a subclass of two-dimensional lattices via characteristic Lie rings
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 …
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
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 …
discrete and two continuous variables. By integrability, we mean the presence of reductions …
[PDF][PDF] Algebraic entropy for systems of quad equations
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 …
equations. In particular, I observe that since systems of multilinear equations can have …
Integrability conditions for two-dimensional Toda-like equations
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 …
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
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 …
Darboux integrable by constructing their first integrals. This result explains why the rate of …
Integrability of difference equations through algebraic entropy and generalized symmetries
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 …
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
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 …
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 …
от одной дискретной и двух непрерывных переменных. Под интегрируемостью …