[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 …

Novel soliton molecule solutions for the second extend (3+ 1)-dimensional Jimbo-Miwa equation in fluid mechanics

H Ma, X Chen, A Deng - Communications in Theoretical Physics, 2023‏ - iopscience.iop.org
The main aim of this paper is to investigate the different types of soliton molecule solutions of
the second extend (3+ 1)-dimensional Jimbo-Miwa equation in a fluid. Four different …

Generalized symmetry classification of discrete equations of a class depending on twelve parameters

RN Garifullin, RI Yamilov - Journal of Physics A: Mathematical …, 2012‏ - iopscience.iop.org
We carry out the generalized symmetry classification of polylinear autonomous discrete
equations defined on the square, which belong to a twelve-parametric class. The direct …

On Symmetries of Integrable Quadrilateral Equations

J Cheng, J Liu, D Zhang - Symmetry, 2024‏ - mdpi.com
In the paper, we describe a method for deriving generalized symmetries for a generic
discrete quadrilateral equation that allows a Lax pair. Its symmetry can be interpreted as a …

Classification of five-point differential-difference equations

RN Garifullin, RI Yamilov, D Levi - Journal of Physics A …, 2017‏ - iopscience.iop.org
Using the generalized symmetry method, we carry out, up to autonomous point
transformations, the classification of integrable equations of a subclass of the autonomous …

Recursion operators, conservation laws, and integrability conditions for difference equations

AV Mikhailov, JP Wang, P Xenitidis - Theoretical and Mathematical …, 2011‏ - Springer
We attempt to propose an algebraic approach to the theory of integrable difference
equations. We define the concept of a recursion operator for difference equations and show …

Classification of five-point differential–difference equations II

RN Garifullin, RI Yamilov, D Levi - Journal of Physics A …, 2018‏ - iopscience.iop.org
Using the generalized symmetry method we finish a classification, started in article
(Garifullin et al 2017 J. Phys. A: Math. Theor. 50 125201), of integrable autonomous five …

Generalized symmetry integrability test for discrete equations on the square lattice

D Levi, RI Yamilov - Journal of Physics A: Mathematical and …, 2011‏ - iopscience.iop.org
We present an integrability test for discrete equations on the square lattice, which is based
on the existence of a generalized symmetry. We apply this test to a number of equations …

Symmetry-preserving numerical schemes

A Bihlo, F Valiquette - Symmetries and Integrability of Difference Equations …, 2017‏ - Springer
In these lectures we review two procedures for constructing finite difference numerical
schemes that preserve symmetries of differential equations. The first approach is based on …

[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 …