Quantum lattice KdV equation (Q1354890)

An example of a completely integrable ``discrete spacetime quantum model'' whose Heisenberg equations of motion determine the evolution generators \(\varphi_n(\tau)\) is presented. A set of Fateev-Zamolodchikov \(R\)-matrices satisfying a chain of Yang-Baxter equations is considered, and the integrability of the Heisenberg equations is studied. It is shown that these equations can be considered as a lattice counterpart of numerous integrable equations, including that of Korteweg-de Vries. Finally, the uniqueness of the model presented in the paper is discussed.