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Kostyantyn Zheltukhın

Department of Mathematics
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...
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 ...