An affine sl(n + 1) algebraic construction of the basic constrained KP
hierarchy is presented. This hierarchy is analyzed using two approach
es, namely linear matrix eigenvalue problem on hermitian symmetric spa
ce and constrained KP Lax formulation and it is shown that these appro
aches are equivalent. The model is recognized to be the generalized no
n-linear Schrodinger (GNLS) hierarchy and it is used as a building blo
ck for a new class of constrained KP hierarchies. These constrained KP
hierarchies are connected via similarity-Backlund transformations and
interpolate between GNLS and multi-boson KP-Toda hierarchies. Our con
struction uncovers the origin of the Toda lattice structure behind the
latter hierarchy. (C) 1995 American Institute of Physics.