Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 138

Doubly discrete Lagrangian systems related to the Hirota and Sine-Gordon equation

C. Emmrich, N. Kutz

We extend the action for evolution equations of KdV and MKdV type which was derived in [Capel, Nijhoff:"Integrable Quantum Mappings"] to the case of not periodic, but only equivariant phase space variables, introduced in [Faddeev, Volkov: Hirota Equation as an Example of an Integrable Symplectic Map]. The difference of these variables may be interpreted as reduced phase space variables via a Marsden- Weinstein reduction where the monodromies play the role of a momentum map. As an example we obtain the doubly discrete sine-Gordon equation and the Hirota equation and the corressponding symplectic structures.

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