Hamiltonian formulation of SL(3) Ur - KdV equation
Jun, 199311 pages
Published in:
- Mod.Phys.Lett.A 8 (1993) 2927-2936
e-Print:
- hep-th/9308071 [hep-th]
Report number:
- KHTP-93-03,
- SNUTP-93-21
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Abstract:
We give a unified view of the relation between the 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 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.- Korteweg-de Vries equation: SL(3)
- Boussinesq equation
- Hamiltonian formalism
- differential equations: Lax
- Miura transformation
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