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arXiv · hep-th/9308071

Hamiltonian formulation of SL(3) Ur-KdV equation

B. K. Chung·K. G. Joo·Soonkeon Nam
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Abstract

We give a unified view of the relation between the $SL(2)$ KdV, the mKdV, and the Ur-KdV equations through the Fréchet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no non-local operators. We extend this method to the $SL(3)$ KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian structure of Ur-Bsq equationin a simple form. In particular, we explicitly construct the hamiltonian operator of the Ur-Bsq system which defines the poisson structure of the system, through the Fréchet derivative and its inverse.

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B. K. Chung, K. G. Joo, Soonkeon Nam. 1993-08-16. Hamiltonian formulation of SL(3) Ur-KdV equation. https://doi.org/10.1142/s0217732393003342

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