Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1997-08-20
Int. J. Mod. Phys. A13 (1998) 2723
Nonlinear Sciences
Exactly Solvable and Integrable Systems
14 pages, RevTex, no figures, typos corrected
Scientific paper
10.1142/S0217751X98001384
We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$ algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian structure of the nonstandard multi-constraint KP hierarchy can be simplified by factorizing its Lax operator to multiplication form. We then diagonalize this simplified Poisson matrix and obtain the free-field realizations of its associated nonlocal algebras.
Shaw Jiin-Chang
Tu Ming-Hsien
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