37 citations · 142 across the 19 of their papers we have counts for
20 papers
Negative Hierarchy of Hydrodynamic Type Equations
Kostyantyn Zheltukhin
The negative integrable hierarchies of shallow water waves and dispersionless Toda lattice equations are considered. The integrability is shown by explicit construction of an infin…
On construction of discrete Darboux integrable equations
Kostyantyn Zheltukhin, Natalya Zheltukhina
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discre…
On the discretization of Darboux Integrable Systems admitting the second-order integrals
Kostyantyn Zheltukhin, Natalya Zheltukhina
We study discretization of Darboux integrable systems. The discretization is done by using - or -integrals of the considered systems. New examples of semi-discrete Darboux in…
Discrete Symmetries and Nonlocal Reductions
Metin Gürses, Aslı Pekcan, Konstyantyn Zheltukhin
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
Nonlocal Hydrodynamic Type of Equations
Metin Gürses, Aslı Pekcan, Konstyantyn Zheltukhin
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.…
On the discretization of Darboux Integrable Systems
Kostyantyn Zheltukhin, Natalya Zheltukhina
We study the discretization of Darboux integrable systems. The discretization is done using -, -integrals of the considered continuous systems. New examples of semi-discrete…