Determinant and Pfaffian solutions of the strong coupling limit of integrable discrete NLS systems

The strong coupling limits of the integrable semi-discrete and fully discrete nonlinear Schrödinger systems are studied by using the Hirota bilinear method. The determinant solutions (in both infinite and finite lattice cases) for the strong coupling limits of semi-discrete and fully discrete nonlinear Schrödinger systems are obtained using a determinant technique. The vector generalizations of the strong coupling limits of semi-discrete and fully discrete nonlinear Schrödinger systems are also presented. The Pfaffian solutions for vector systems are obtained using the Pfaffian technique.