Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation

Details Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation

2005-06-24

arxiv.org/abs/nlin/0506052v3

J. Phys. Soc. Jpn., Vol.75, No. 5 (2006) p.054002

Nonlinear Sciences

Exactly Solvable and Integrable Systems

First version was uploaded in 23 Jun 2005. Published in Journal of the Physical Society of Japan in May, 2006

Scientific paper

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.

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