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.

Keywords:

• Semi-discrete chain
• Darboux integrability
• x-integral
• n-integral
• continuum limit
• discretization

2000 Mathematics Subject Classification:

• 35Q51
• 37K60