Adler{endash}Kostant{endash}Symes construction, bi-Hamiltonian manifolds, and KdV equations
- Max Planck Institut fuer Mathematik, Gottfried Claren Str. 26, D-53225 Bonn (Germany)
This paper focuses a relation between Adler{endash}Kostant{endash}Symes (AKS) theory applied to Fordy{endash}Kulish scheme and bi-Hamiltonian manifolds. The spirit of this paper is closely related to Casati{endash}Magri{endash}Pedroni work on Hamiltonian formulation of the KP equation. Here the KdV equation is deduced via the superposition of the Fordy{endash}Kulish scheme and AKS construction on the underlying current algebra C{sup {infinity}}(S{sup 1},g{circle_times}{bold C}[[{lambda}]]). This method is different from the Drinfeld{endash}Sokolov reduction method. It is known that AKS construction is endowed with bi-Hamiltonian structure. In this paper we show that if one applies the Fordy{endash}Kulish construction in the Adler{endash}Kostant{endash}Symes scheme to construct an integrable equation associated with symmetric spaces then this superposition method becomes closer to Casati{endash}Magri{endash}Pedroni{close_quote}s bi-Hamiltonian method of the KP equation. We also add a self-contained Appendix, where we establish a direct relation between AKS scheme and bi-Hamiltonian methods. {copyright} {ital 1997 American Institute of Physics.}
- OSTI ID:
- 542578
- Journal Information:
- Journal of Mathematical Physics, Vol. 38, Issue 10; Other Information: PBD: Oct 1997
- Country of Publication:
- United States
- Language:
- English
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