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

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

1994-09-23

arxiv.org/abs/hep-th/9409144v1

Phys. Lett. A201:156-160,1995

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, Sfb288 Preprint 139

Scientific paper

10.1016/0375-9601(95)00233-S

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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