On a discrete Davey-Stewartson system
  We propose a differential difference equation in ${\mathcal R}^1\times {\mathcal Z}^2$ and study it by   Hirota's bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B\"{a}cklund transformation which enables us to obtain its Lax pair. 
Gegenhasi, Xing-Biao Hu and Decio Levi