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Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the $2n$-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for $n\times n$ matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato–Wilson relations. A reduction process leads to the AKNS, two-component Camassa–Holm and Cecotti–Vafa models and the formalism provides simple formulas for their solutions.
Keywords: Clifford algebra; tau-functions; Kac–Moody algebras; loop groups; Camassa–Holm equation; Cecotti–Vafa equations; AKNS hierarchy. 
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     author = {Henrik Aratyn and Johan van de Leur},
     title = {Clifford {Algebra} {Derivations} of {Tau-Functions} for {Two-Dimensional} {Integrable} {Models} with {Positive} and {Negative} {Flows}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a19/}
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Henrik Aratyn; Johan van de Leur. Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a19/

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