Lax Pairs for Discrete Integrable Equations via Darboux Transformations

A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler–Bobenko–Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations.