Show/Hide Menu
Hide/Show Apps
anonymousUser
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Videos
Videos
Thesis submission
Thesis submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Contact us
Contact us
Kostyantyn Zheltukhın
E-mail
zheltukh@metu.edu.tr
Department
Department of Mathematics
Publications
Theses Advised
Open Courses
Projects
On the discretization of Darboux Integrable Systems
Zheltukhın, Kostyantyn; ZHELTUKHİNA, NATALYA (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, METİN; 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; ZHELTUKHİNA, NATALYA (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; ZHELTUKHİNA, NATALYA; 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; ZHELTUKHİNA, NATALYA (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; ZHELTUKHİNA, NATALYA (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.
Cartan matrices and integrable lattice Toda field equations
Habibullin, Ismagil; Zheltukhın, Kostyantyn; Yangubaeva, Marina (IOP Publishing, 2011-11-18)
Differential-difference integrable exponential-type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras A(2), B(2), C(2), G(2), the ...
Dynamical systems and Poisson structures
Guerses, Metin; Guseinov, Gusein Sh; Zheltukhın, Kostyantyn (AIP Publishing, 2009-11-01)
We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical ...
F
P
1
2
N
E
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX