Casorati Determinant Form of Dark Soliton Solutions of the Discrete   Nonlinear Schr\"odinger Equation
  It is shown that the $N$-dark soliton solutions of the integrable discrete nonlinear Schr\"odinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy and regularity for the Casorati determinant solution are also given explicitly. The relationship between the IDNLS and the relativistic Toda lattice is discussed. 
Ken-ichi Maruno and Yasuhiro Ohta