Singular sector of the Kadomtsev-Petviashvili hierarchy, (partial derivative)over-bar operators of nonzero index, and associated integrable systems

Integrable hierarchies associated with the singular sector of the Kadomtsev -Petviashvili (KP) hierarchy, or equivalently, with <(partial derivative)ov er bar> operators of nonzero index are studied. They arise as the restricti on of the standard KP hierarchy to submanifolds of finite codimension in th e space of independent variables. For higher <(partial derivative)over bar> index these hierarchies represent themselves as families of multidimension al equations with multidimensional constraints. The <(partial derivative)ov er bar>-dressing method is used to construct these hierarchies. Hidden Kort eweg-de Vries, Boussinesq, and hidden Gelfand-Dikii hierarchies are conside red, too. (C) 2000 American Institute of Physics. [S0022-2488(99)02812-1].