40 citations · 240 across the 22 of their papers we have counts for
22 papers
On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries
R. N. Garifullin, I. T. Habibullin
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continu…
Hyperbolic equations with fifth-order symmetries
Rustem N. Garifullin
This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\part…
On a class of exact solutions of the Ishimori equation
Rustem N. Garifullin, Ismagil T. Habibullin
In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which…
Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations
Rustem N. Garifullin, Ismagil T. Habibullin
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for…
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…
On the integrability of a discrete analogue of the Kaup-Kupershmidt equation
R. N. Garifullin, R. I. Yamilov
We study a new example of equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of one-dimension…
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…
Peculiar symmetry structure of some known discrete nonautonomous equations
Rustem N. Garifullin, Ismagil T. Habibullin, Ravil I. Yamilov
We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely dis…
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…
Affine Lie algebras, Lax pairs and integrable discrete and continuous systems
Rustem N. Garifullin, Ismagil T. Habibullin
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial diffe…
Generalized symmetry classification of discrete equations of a class depending on twelve parameters
Rustem N. Garifullin, Ravil I. Yamilov
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 result…
Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
Rustem Garifullin, Ismagil Habibullin, Marina Yangubaeva
Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras , , , , …
Method for searching higher symmetries for quad graph equations
Rustem N. Garifullin, Elena V. Gudkova, Ismagil T. Habibullin
Generalized symmetry integrability test for discrete equations on the square lattice is studied. Integrability conditions are discussed. A method for searching higher symmetries (i…
Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation
R. Garifullin, B. Suleimanov, N. Tarkhanov
We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.