On a Two-Parameter Extension of the Lattice KdV System Associated with an Elliptic Curve

A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal) elliptic Cauchy kernel. The consistency and integrability of the lattice system is discussed as well as special solutions and associated continuum equations. 1Introduction In recent years the integrability of discrete equations, i.e. ordinary or partial difference equations as well as analytic difference equations, has become an issue of considerable attention (cf. the biannual sequel of SIDE meetings on Symmetries and Integrability of Difference Equations,