Browsing by Keywords "Darboux integrability"
Now showing items 1-6 of 6
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Characteristic lie algebra and classification of semi-discrete models
(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
(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
(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
(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
(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
(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 ...
