25 citations · 92 across the 10 of their papers we have counts for
11 papers
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…
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…
Semi-discrete hyperbolic equations admitting five dimensional characteristic -ring
Kostyantyn Zheltukhin, Natalya Zheltukhina
The necessary and sufficient conditions for a hyperbolic semi-discrete equation to have five dimensional characteristic {\it x}-ring are derived. For any given chain, the derived c…
Discretization of Liouville type nonautonomous equations preserving integrals
Ismagil Habibullin, Natalya Zheltukhina
The problem of constructing semi-discrete integrable analogues of the Liouville type integrable PDE is discussed. We call the semi-discrete equation a discretization of the Liouvil…
Discretization of hyperbolic type Darboux integrable equations preserving integrability
Ismagil Habibullin, Natalya Zheltukhina, Alfia Sakieva
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models…