Browsing by Subject "x-integral"
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Item Open Access Discretization of Liouville type nonautonomous equations preserving integrals(Taylor and Francis, 2016) Habibullin, I.; Zheltukhina, N.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 common integral. For the Liouville type integrable equations from the well-known Goursat list for which the integrals of minimal order are of the order less than or equal to two we presented a list of corresponding semi-discrete versions. The list contains new examples of non-autonomous Darboux integrable chains. © 2016 the authors.Item Open Access On the discretization of Laine equations(Taylor and Francis, 2018) Zheltukhin, K.; Zheltukhina, NatalyaWe 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 an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable.