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@prefix dct: <http://purl.org/dc/terms/> .
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              Fay's identity on Riemann surfaces is a powerful tool in the context of algebro-geometric solutions to integrable equations. This relation generalizes a well-known identity for the cross-ratio function in the complex plane. It allows to establish relations between theta functions and their derivatives. This offers a complementary approach to algebro-geometric solutions of integrable equations with certain advantages with respect to the use of Baker-Akhiezer functions. It has been successfully applied by Mumford et al. to the Korteweg-de Vries, Kadomtsev-Petviashvili and sine-Gordon equations. Following this approach, we construct algebro-geometric solutions to the Camassa-Holm and Dym type equations, as well as solutions to the multi-component nonlinear Schrödinger equation and the Davey-Stewartson equations. Solitonic limits of these solutions are investigated when the genus of the associated Riemann surface drops to zero. Moreover, we present a numerical evaluation of algebro-geometric solutions of integrable equations when the associated Riemann surface is real.
            """ ;
    dct:identifier "NNT: 2011DIJOS020" ;
    dct:issued "2026-05-26T04:38:49.451842"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-26T04:38:49.451853"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Fay's identity in the theory of integrable systems" ;
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    dcat:keyword "algorithme-de-tretkoff-tretkoff",
        "application-duniformisation",
        "base-dhomologie",
        "breather-rationnel",
        "courbe-algebrique",
        "degenerescence-de-surface-de-riemann",
        "edp",
        "equation-de-camassa-holm",
        "equation-de-davez-stewartson",
        "equation-de-schrodinger-non-lineaire-vectorielle",
        "fonction-theta",
        "identite-de-fay",
        "infoeu-reposemanticsdoctoralthesis",
        "mathmath-gmmathematics-mathgeneral-mathematics-mathgm",
        "no-english-keywords",
        "ovale-reel",
        "periodes-de-differentielles-holomorphes",
        "soliton",
        "solutions-algebro-geometriques",
        "surface-de-riemann",
        "theses",
        "theta-diviseur" ;
    dcat:landingPage <https://theses.hal.science/tel-00622289> .

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    dct:issued "2026-05-26T04:38:49.472914"^^xsd:dateTime ;
    dct:modified "2026-05-26T04:38:49.374558"^^xsd:dateTime ;
    dct:title "Fay's identity in the theory of integrable systems" ;
    dcat:accessURL <https://theses.hal.science/tel-00622289> .

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