Discretization of Liouville type nonautonomous equations preserving integrals

Abstract

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.

27 pages

References in corpus (3)

• Generalized symmetry classification of discrete equations of a class depending on twelve parameters
• On the Classification of Darboux Integrable Chains
• Discretization of hyperbolic type Darboux integrable equations preserving integrability