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

Boris G. Konopelchenko; Luis Martinez Alonso; Elena Medina

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

Boris G. Konopelchenko·Luis Martinez Alonso·Elena Medina

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Abstract

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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Boris G. Konopelchenko, Luis Martinez Alonso, Elena Medina. 1998-05-29. Singular sector of the KP hierarchy, $\bar{\partial}$-operators of non-zero index and associated integrable systems. https://arxiv.org/abs/solv-int/9806001

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