Abstract
We investigate the bi-Hamiltonian structures associated with constrained dispersionless modified Kadomtsev–Petviashvili (KP) hierarchies which are constructed from truncations of the Lax operator of the dmKP hierarchy. After transforming their second Hamiltonian structures to those of the Gelfand–Dickey-type, we obtain the Poisson algebras of the coefficient functions of the truncated Lax operators. Then we study the conformal property and free-field realizations of these Poisson algebras. Some examples are worked out explicitly to illustrate the obtained results.
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