Hamiltonian formulation of SL(3) Ur-KdV equation

Details Hamiltonian formulation of SL(3) Ur-KdV equation Hamiltonian formulation of SL(3) Ur-KdV equation

1993-08-16

arxiv.org/abs/hep-th/9308071v1

Mod.Phys.Lett.A8:2927-2936,1993

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, KHTP-93-03 SNUTP-93-21

Scientific paper

10.1142/S0217732393003342

We give a unified view of the relation between the $SL(2)$ KdV, the mKdV, and the Ur-KdV equations through the Fr\'{e}chet 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 Fr\'{e}chet derivative and its inverse.

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