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arXiv · hep-th/9409144

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

C. Emmrich·N. Kutz
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Abstract

We extend the action for evolution equations of KdV and MKdV type which was derived in [Capel/Nijhoff] to the case of not periodic, but only equivariant phase space variables, introduced in [Faddeev/Volkov]. 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 the momentum map. As an example we obtain the doubly discrete sine-Gordon equation and the Hirota equation and the corresponding symplectic structures.

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C. Emmrich, N. Kutz. 1994-09-23. Doubly discrete Lagrangian systems related to the Hirota and Sine-Gordon equation. https://doi.org/10.1016/0375-9601(95)00233-s

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