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We propose a natural (2+1)-dimensional generalization of the Ablowitz-Ladiklattice that is an integrable space discretization of the cubic nonlinearSchroedinger (NLS) system in 1+1 dimensions. By further requiring rotationalsymmetry of order 2 in the two-dimensional lattice, we identify an appropriatechange of dependent variables, which translates the (2+1)-dimensionalAblowitz-Ladik lattice into a suitable space discretization of theDavey-Stewartson system. The space-discrete Davey-Stewartson system has a Laxpair and allows the complex conjugation reduction between two dependentvariables as in the continuous case. Moreover, it is ideally symmetric withrespect to space reflections. Using the Hirota bilinear method, we constructsome exact solutions such as multidromion solutions.

On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system