On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnet

Details On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnet On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnet

1999-06-28

arxiv.org/abs/solv-int/9907002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, LaTeX2e

Scientific paper

The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and
the discrete nonlinear Schr\"odinger equation (NLSE) given by Ablowitz and
Ladik is shown. This is used to derive the equivalence of their discretization
with the one by Izergin and Korepin. Moreover a doubly discrete IHM is
presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.

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