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Construction of KP Hierarchies in Terms of Finite Number of Fields and their Abelianization

H. Aratyn·E. Nissimov·S. Pacheva
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Abstract

The $2M$-boson representations of KP hierarchy are constructed in terms of $M$ mutually independent two-boson KP representations for arbitrary number $M$. Our construction establishes the multi-boson representations of KP hierarchy as consistent Poisson reductions of standard KP hierarchy within the $R$-matrix scheme. As a byproduct we obtain a complete description of any finitely-many-field formulation of KP hierarchy in terms of Darboux coordinates with respect to the first Hamiltonian structure. This results in a series of representations of $\Win1\,$ algebra made out of arbitrary even number of boson fields.

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H. Aratyn, E. Nissimov, S. Pacheva. 1993-06-20. Construction of KP Hierarchies in Terms of Finite Number of Fields and their Abelianization. https://doi.org/10.1016/0370-2693(93)91319-i

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