Coupled Nonlinear Schr\"odinger equation and Toda equation (the Root of Integrability)
Abstract
We consider the relation between the discrete coupled nonlinear Schr\"odinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\"odinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.
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