Poisson Algebras associated with Constrained Dispersionless Modified KP Hierarchies

Abstract

We investigate the bi-Hamiltonian structures associated with constrained dispersionless modified KP hierarchies which are constructed from truncations of the Lax operator of the dispersionless modified KP hierarchy. After transforming their second Hamiltonian structures to those of 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.

15 pages, latex, no figures

References in corpus (2)

• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies

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