On the three‐dimensional consistency of Hirota's discrete Korteweg‐de Vries equation

Abstract

AbstractHirota's discrete Korteweg‐de Vries equation (dKdV) is an integrable partial difference equation on , which approaches the Korteweg‐de Vries equation in a continuum limit. We find new transformations to other equations, including a second‐degree second‐order partial difference equation, which provide an unusual embedding into a three‐dimensional lattice. The consistency of the resulting system extends a property that has been widely used to study partial difference equations on multidimensional lattices.