Browsing by Author "Zheltukhin, K."
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Bipresymplectic chains of corank 1 and related Liouville integrable systems
Błaszak, M.; Gürses, M.; Zheltukhin, K. (Institute of Physics Publishing Ltd., 2009)Bipresymplectic chains of 1forms of corank 1 are considered. The conditions under which such chains represent some Liouville integrable systems and the conditions under which there exist related biHamiltonian chains ... 
Discrete symmetries and nonlocal reductions
Gürses, Metin; Pekcan, A.; Zheltukhin, K. (Elsevier, 2020)We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations. 
Dynamical systems and Poisson structures
Gurses, M.; Guseinov, G. Sh.; Zheltukhin, K. (American Institute of Physics, 2009)We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in ℝ3 are locally biHamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical ... 
Hamiltonian equations in ℝ3
Ay, A.; Gürses, M.; Zheltukhin, K. (AIP Publishing LLC, 200308)The Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in ℝ3 is proposed. The form of the solution is shown to be valid also in the neighborhood of some irregular ... 
Hydrodynamic type of integrable equations on a segment and a half line
Gurses, M.; Habibullin, I.; Zheltukhin, K. (American Institute of Physics, 2008)The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions ... 
Integrable boundary value problems for elliptic Toda lattice in a disk
Gürses M.; Habibulin, I.; Zheltukhin, K. (American Institute of Physics, 2007)The concept of integrable boundary value problems for soliton equations on ℝ and ℝ+ is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lattice and its reductions ... 
Nonlocal hydrodynamic type of equations
Gürses, Metin; Pekcan, A.; Zheltukhin, K. (Elsevier, 20200301)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 ... 
On a class of Darbouxintegrable semidiscrete equations
Zheltukhin, K.; Zheltukhina, N.; Bilen, E. (Springer, 2017)We consider a classification problem for Darbouxintegrable hyperbolic semidiscrete equations. In particular, we obtain a complete description for a special class of equations admitting fourdimensional characteristic ... 
On a transformation between hierarchies of integrable equations
Gürses, M.; Zheltukhin, K. (Elsevier BV * NorthHolland, 2006)A transformation between a hierarchy of integrable equations arising from the standard Rmatrix construction on the algebra of differential operators and a hierarchy of integrable equations arising from a deformation of ... 
On existence of an xintegral for a semidiscrete chain of hyperbolic type
Zheltukhin, K.; Zheltukhina, Natalya (IOP, 2016)A class of semidiscrete chains of the form t1x = f (x,t,t1,tx) is considered. For the given chains easily verifiable conditions for existence of xintegral of minimal order 4 are obtained. 
On the discretization of darboux integrable systems
Zheltukhin, K.; Zheltukhina, Natalya (Taylor and Francis, 2020)We study the discretization of Darboux integrable systems. The discretization is done using x, yintegrals of the considered continuous systems. New examples of semidiscrete Darboux integrable systems are obtained. 
On the discretization of Laine equations
Zheltukhin, K.; Zheltukhina, Natalya (Taylor and Francis, 2018)We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semidiscrete equation which has that integral as an nintegral, or we proved that such ... 
On the integrability of a class of MongeAmpère equations
Brunelli J.C.; Gürses M.; Zheltukhin, K. (World Scientific Publishing Co. Pte. Ltd., 2001)We give the Lax representations for the elliptic, hyperbolic and homogeneous second order MongeAmpère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless ... 
Recursion operator and dispersionless rational Lax representation
Zheltukhin, K. (2002)We consider equations arising from dispersionless rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate biHamiltonian ... 
Recursion operators of some equations of hydrodynamic type
Gürses M.; Zheltukhin, K. (A I P Publishing LLC, 2001)We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N = 2 and N = 3 containing the equations of ... 
Semidiscrete hyperbolic equations admitting five dimensional characteristic xring
Zheltukhin, K.; Zheltukhina, N. (Taylor and Francis Ltd., 2016)The necessary and sufficient conditions for a hyperbolic semidiscrete equation to have five dimensional characteristic xring are derived. For any given chain, the derived conditions are easily verifiable by straightforward ...