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

Abstract

It is shown that the $N$-dark soliton solutions of the integrable discrete nonlinear Schrödinger (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.

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

References in corpus (1)

• Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

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