H. Aratyn et al., CONSTRUCTION OF KP HIERARCHIES IN TERMS OF FINITE NUMBER OF FIELDS AND THEIR ABELIANIZATION, Physics letters. Section B, 314(1), 1993, pp. 41-51
The 2M-boson representations of the KP hierarchy are constructed in te
rms of M mutually independent two-boson KP representations for arbitra
ry number M. Our construction establishes the multi-boson representati
ons of the KP hierarchy as consistent Poisson reductions of the standa
rd KP hierarchy within the R-matrix scheme. As a byproduct we obtain a
complete description of any finitely-many-field formulation of the KP
hierarchy in terms of Darboux coordinates with respect to the first H
amiltonian structure. This results in a series of representations of W
1+infinity algebra made out of an arbitrary even number of boson field
s.