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

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

1998-05-29

arxiv.org/abs/solv-int/9806001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

45 pages, LaTeX 2.09 with epsf,amstex and amssymb styles

Scientific paper

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.

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