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Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schr\"odinger Equation
Preprint
2005-06-23
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Abstract
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.