Coupled Nonlinear Schrödinger equation and Toda equation (the Root of Integrability)

Abstract

We consider the relation between the discrete coupled nonlinear Schrödinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schrödinger 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.

11 pages, LateX, to apper in J. Phys. Soc. Jpn. Vol. 66, No 7

References in corpus (1)

• Faces of Relativistic Toda Chain

Cited by in corpus (3)

• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
• On vector analogs of the modified Volterra lattice
• The Davey Stewartson system and the Bäcklund Transformations