Hamiltonian formulation of SL(3) Ur-KdV equation
arXiv:hep-th/9308071 · doi:10.1142/S0217732393003342
Abstract
We give a unified view of the relation between the 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 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.
12 pages, KHTP-93-03 SNUTP-93-21