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A bilinearisation-reduction approach is described for finding solutions fornonlocal integrable systems and is illustrated with nonlocal discrete nonlinearSchr\"odinger equations. In this approach we first bilinearise the coupledsystem before reduction and derive its double Casoratian solutions, then weimpose reduction on double Casoratians so that they coincide with the nonlocalreduction on potentials. Double Caosratian solutions of the classical andnonlocal (reverse space, reverse time and reverse space-time) discretenonlinear Schr\"odinger equations are presented.

Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schr\"odinger equations