Singular sector of the KP hierarchy, ∂̄-operators of non-zero index and associated integrable systems
نویسندگان
چکیده
Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with ∂̄-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 ∂̄-index these hierarchies represent themselves families of multidimensional equations with multidimensional constraints. The ∂̄-dressing method is used to construct these hierarchies. Hidden KdV, Boussinesq and hidden Gelfand-Dikii hierarchies are considered too.
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