Nonautonomous discrete integrable systems

It is explained how a description of integrable systems using fermion operators leads in a natural way to the notions of Darboux and binary Darboux transformations. This approach is illustrated for a nonautonomous version of the discrete KP (dKP) equation. As an application of this technique, solutions – some of which are expressed in terms of special functions – are discussed. The ultra-discrete limit is then performed to obtain a nonautonomous ultra-discrete system with particularly interesting soliton behaviour.