44 citations · 220 across the 19 of their papers we have counts for
19 papers
Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure
R. N. Garifullin, R. I. Yamilov
In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of integrable discrete autonomous equations on a square lattice with a non-standard structure of generalize…
On a series of Darboux integrable discrete equations on the square lattice
R. N. Garifullin, R. I. Yamilov
We present a series of Darboux integrable discrete equations on the square lattice. Equations of the series are numbered with natural numbers . All the equations have a first in…
Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
Rustem N. Garifullin, Ravil I. Yamilov
We consider five-point differential-difference equations. Our aim is to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discr…
Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
R. N. Garifullin, G. Gubbiotti, R. I. Yamilov
In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Ya…
An unusual series of autonomous discrete integrable equations on the square lattice
R. N. Garifullin, R. I. Yamilov
We present an infinite series of autonomous discrete equations on the square lattice possessing hierarchies of autonomous generalized symmetries and conservation laws in both direc…
On the integrability of a lattice equation with two continuum limits
R. N. Garifullin, R. I. Yamilov
We study a new example of lattice equation being one of the key equations of a recent generalized symmetry classification of five-point differential-difference equations. This equa…
Classification of five-point differential-difference equations II
R. N. Garifullin, R. I. Yamilov, D. Levi
Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-diffe…
Darboux Integrability of Trapezoidal and Families of Lattice Equations II: General Solutions
Giorgio Gubbiotti, Christian Scimiterna, Ravil I. Yamilov
In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal equations and the equations. These solutions are obtained…
Classification of five-point differential-difference equations
R. N. Garifullin, R. I. Yamilov, D. Levi
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point d…
Non-invertible transformations for the classification of differential-difference equations
R. N. Garifullin, R. I. Yamilov, D. Levi
We discuss aspects of the theory of non-invertible transformations which enter in the problem of classification of diffe\-ren\-tial-difference equations and, in particular, the not…
Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
R. N. Garifullin, R. I. Yamilov
We construct integrable discrete nonautonomous quad-equations as Bäcklund auto-transformations for known Volterra and Toda type semidiscrete equations, some of which are also nonau…
Examples of Darboux Integrable Discrete Equations Possessing First Integrals of an Arbitrarily High Minimal Order
Rustem N. Garifullin, Ravil I. Yamilov
We consider a discrete equation, defined on the two-dimensional square lattice, which is linearizable, namely, of the Burgers type and depends on a parameter . For any natural n…
Generalized symmetry integrability test for discrete equations on the square lattice
D. Levi, R. I. Yamilov
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 equation…
Integrability Test for Discrete Equations via Generalized Symmetries
D. Levi, R. I. Yamilov
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial di…
Lie point symmetries of differential--difference equations
D. Levi, P. Winternitz, R. Yamilov
We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete…
The Generalized Symmetry Method for Discrete Equations
D. Levi, R. I. Yamilov
The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we…
On a nonlinear integrable difference equation on the square 3D-inconsistent
D. Levi, R. I. Yamilov
We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra diffe…
Classification of evolutionary equations on the lattice. I. The general theory
D. Levi, R. Yamilov
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form where is…
Bäcklund transformation and the construction of the integrable boundary-value problem for the equation
R. A. Sharipov, R. I. Yamilov
Bäcklund transformation for the Bullough-Dodd-Jiber-Shabat equation is found. The construction of integrable boundary condition for this equation togeth…