Bilinear identities and discrete equations

Discrete counterparts of integrable systems are obtained from bilinear identities resulting from expanding typical solutions which appear in the form of Casorati and multi-Casorati determinants. The method of analyzing the bilinear equations that come from Laplace expansions has produced potentially-integrable discrete systems. The aim has been to concentrate on the equations at the bilinear level rather than to investigate what happens when they are turned into nonlinear equations. However, the three-component case studied turns out to correspond to the three-dimensional quadrilateral lattice of M. Manas, A. Doliwa, and P.M. Santini, which is known to be integrable by construction.