JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, vol.25, no.1, pp.166-177, 2018 (SCI-Expanded)
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 an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable.