Geodesic
Geometric solutions of the strict KP hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 54-78
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Splitting the algebra Psd of pseudodifferential operators into the Lie subalgebra of all differential operators without a constant term and the Lie subalgebra of all integral operators leads to an integrable hierarchy called the strict KP hierarchy. We consider two Psd modules, a linearization of the strict KP hierarchy and its dual, which play an essential role in constructing solutions geometrically. We characterize special vectors, called wave functions, in these modules; these vectors lead to solutions. We describe a relation between the KP hierarchy and its strict version and present an infinite-dimensional manifold from which these special vectors can be obtained. We show how a solution of the strict KP hierarchy can be constructed for any subspace $W$ in the Segal–Wilson Grassmannian of a Hilbert space and any line $\ell$ in $W$. Moreover, we describe the dual wave function geometrically and present a group of commuting flows that leave the found solutions invariant.
Keywords: pseudodifferential operator, KP hierarchy, strict KP hierarchy, (dual) linearization, (dual) oscillating function, (dual) wave function, Grassmannian. 
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G. F. Helminck; E. A. Panasenko. Geometric solutions of the strict KP hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 54-78. http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a3/

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