Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows

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dc.creatorAratyn, Henrik
dc.creatorvan de Leur, Johan
dc.date2006-05-12
dc.date2007-02-12
dc.date.accessioned2026-07-07T09:34:39Z
dc.date.available2026-07-07T09:34:39Z
dc.descriptionWe 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
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/nlin/0605027
dc.identifierhttp://arxiv.org/abs/nlin/0605027
dc.identifierSIGMA 3 (2007), 020, 29 pages
dc.identifierdoi:10.3842/SIGMA.2007.020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159570
dc.subjectExactly Solvable and Integrable Systems
dc.subjectAstrophysics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleClifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
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