Singular sector of the KP hierarchy, $\bar{\partial}$-operators of non-zero index and associated integrable systems

Konopelchenko, Boris G.; Alonso, Luis Martinez; Medina, Elena

Singular sector of the KP hierarchy, $\bar{\partial}$-operators of non-zero index and associated integrable systems

Authors

Konopelchenko, Boris G.

Alonso, Luis Martinez

Medina, Elena

Description

Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with $\dbar$-operators of non-zero index are studied. They arise as the restriction of the standard KP hierarchy to submanifols of finite codimension in the space of independent variables. For higher $\dbar$-index these hierarchies represent themselves families of multidimensional equations with multidimensional constraints. The $\dbar$-dressing method is used to construct these hierarchies. Hidden KdV, Boussinesq and hidden Gelfand-Dikii hierarchies are considered too.
45 pages, LaTeX 2.09 with epsf,amstex and amssymb styles