Now showing items 1-6 of 6

    • Characteristic lie algebra and classification of semi-discrete models 

      Pekcan, Aslı (Bilkent University, 2009)
      In this thesis, we studied a differential-difference equation of the following form tx(n + 1, x) = f(t(n, x), t(n + 1, x), tx(n, x)), (1) where the unknown t = t(n, x) is a function of two independent variables: discrete n ...
    • Discretization of Liouville type nonautonomous equations preserving integrals 

      Habibullin, I.; Zheltukhina, N. (Taylor and Francis, 2016)
      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 Liouville type PDE if these two equations have a ...
    • On a class of Darboux-integrable semidiscrete equations 

      Zheltukhin, K.; Zheltukhina, N.; Bilen, E. (Springer, 2017)
      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 ...
    • On some algebraic properties of semi-discrete hyperbolic type equations 

      Habibullin, Ismagil; Pekcan, Aslı; Zheltukhina, Natalya (Scientific and Technical Research Council of Turkey (TUBITAK), 2008)
      Nonlinear semi-discrete equations of the form tx(n + 1) = f(t(n),t(n + 1),tx(n)) are studied. An adequate algebraic formulation of the Darboux integrability is discussed and an attempt to adopt this notion to the classification ...
    • On the discretization of Laine equations 

      Zheltukhin, K.; Zheltukhina, N. (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 semi-discrete equation which has that integral as an n-integral, or we proved that such ...
    • Semi-discrete hyperbolic equations admitting five dimensional characteristic x-ring 

      Zheltukhin, K.; Zheltukhina, N. (Taylor and Francis Ltd., 2016)
      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 straightforward ...