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Kostyantyn Zheltukhın
E-mail
zheltukh@metu.edu.tr
Department
Department of Mathematics
ORCID
0000-0002-1098-7369
Scopus Author ID
6603497099
Web of Science Researcher ID
AAZ-6715-2020
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ON CONSTRUCTION OF DARBOUX INTEGRABLE DISCRETE MODELS
Zheltukhın, Kostyantyn; Zheltukhina, Natalya (2023-12-01)
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the co...
ON DISCRETIZATION OF DARBOUX INTEGRABLE SYSTEMS ADMITTING SECOND-ORDER INTEGRALS
Zheltukhın, Kostyantyn (2021-01-01)
© 2021 K. Zheltukhin N. Zheltukhina. All Rights Reserved.We consider a discretization problem for hyperbolic Darboux integrable systems. In particular, we discretize continuous systems admitting x- and y-integrals of the f...
On the discretization of Darboux Integrable Systems
Zheltukhın, Kostyantyn (Informa UK Limited, 2020-10-01)
We study the discretization of Darboux integrable systems. The discretization is done using x-, y-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
Nonlocal hydrodynamic type of equations
Gürses, Metin; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-06-01)
We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of hydr...
Discrete symmetries and nonlocal reductions
GÜRSES, METİN; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-01-31)
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
On the discretization of Laine equations
Zheltukhın, Kostyantyn (2018-01-01)
We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation which has that integral as an n-integral, or we proved that such ...
On a class of Darboux-integrable semidiscrete equations
Zheltukhın, Kostyantyn; Bilen, Ergun (Springer Science and Business Media LLC, 2017-06-27)
We consider a classification problem for Darboux-integrable hyperbolic semidiscrete equations. In particular, we obtain a complete description for a special class of equations admitting four-dimensional characteristic x-ri...
RECURSION OPERATOR FOR A SYSTEM WITH NON-RATIONAL LAX REPRESENTATION
Zheltukhın, Kostyantyn (2016-06-01)
We consider a hydrodynamic type system, waterbag model, that admits a dispersionless Lax representation with a logarithmic Lax function. Using the Lax representation, we construct a recursion operator of the system. We not...
Semi-discrete hyperbolic equations admitting five dimensional characteristic x-ring
Zheltukhın, Kostyantyn (2016-01-01)
The necessary and sufficient conditions for a hyperbolic semi-discrete equation to have five dimensional characteristic x-ring are derived. For any given chain, the derived conditions are easily verifiable by straightforwa...
On existence of an x-integral for a semi-discrete chain of hyperbolic type
Zheltukhın, Kostyantyn (IOP Publishing; 2015-06-27)
A class of semi-discrete chains of the form t1x = f(x, t, t1, tx) is considered. For the given chains easily verifiable conditions for existence of x-integral of minimal order 4 are obtained.
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