Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schrodinger equations

A bilinearisation-reduction approach is described for finding solutions for nonlocal integrable systems and is illustrated with nonlocal discrete nonlinear Schrodinger equations. In this approach we first bilinearise the coupled system before reduction and derive its double Casoratian solutions; then we impose reduction on double Casoratians so that they coincide with the nonlocal reduction on potentials. Double Caosratian solutions of the classical and nonlocal (reverse space, reverse time and reverse space-time) discrete nonlinear Schrodinger equations are presented. (C) 2018 Elsevier Inc. All rights reserved.