(2+1)-dimensional Davey-Stewartson I description in a 2D lattice model

The paper is devoted to investigate a two-dimensional (2D) lattice model with interactions between the first- and second-nearest neighbors, which is extracted from a cubic lattice of cystalline alloys. With the help of the method of multiple scales combined with a quasidiscreteness approximation, the (2+1)-dimensional Davey-Stewartson-I (DS-I) equation is obtained from the original 2D discrete system, which is completely integrable and admits explicit solutions such as positon solutions (which are locally singular) and dromions (which decay exponentially in all spatial directions). Then the leading order-approximated solutions of the 2D lattice are constructed by the explicit solutions of the DS-I.