Darboux transformations for the KP hierarchy in the Segal-Wilson setting (Q2715671)
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scientific article; zbMATH DE number 1599828
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Darboux transformations for the KP hierarchy in the Segal-Wilson setting |
scientific article; zbMATH DE number 1599828 |
Statements
20 May 2001
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KP hierarchy
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Darboux transformation
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Grassmann manifold
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nonlinear differential equations
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Darboux transformations for the KP hierarchy in the Segal-Wilson setting (English)
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The KP hierarchy consists of a tower of nonlinear differential equations in infinitely many variables \(\{t_n\mid n\geq 1\}\). This paper shows that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the KP hierarchy corresponding to these planes. Also, the original results include: a closed form of the operators that procure the transformation, the related geometric data expressing the operators, and the associated transformation on the level of \(\tau\)-functions.
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