@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              In this paper, I construct the Darboux transformations for the non-commutative Toda solutions at n = 1 with the help of linear systems whose compatibility condition yields zero curvature representation of associated systems of non-linear differential equations. I also derive the quasideterminant solutions of the non-commutative Painlevé II equation by taking the Toda solutions at n = 1 as a seed solution in its Darboux transformations. Further by iteration, I generalize the Darboux transformations of the seed solutions to N-th form. At the end I describe the zero curvature representation of quantum Painlevé II equation that involves Planck constant h explicitly and system reduces to the classical Painlevé II when h → 0.
            """ ;
    dct:identifier "hal-00983782" ;
    dct:issued "2026-05-05T12:22:47.780231"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-05T12:22:47.780235"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Quasideterminant solutions of NC Painlevé II equation with the Toda solution at n= 1 as a seed solution in its Darboux transformation" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
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    dcat:keyword "darboux-transformation",
        "infoeu-reposemanticspreprint",
        "integrable-systems",
        "mathmath-mpmathematics-mathmathematical-physics-math-ph",
        "painleve-ii-equation",
        "preprints-working-papers-",
        "riccati-equation",
        "toda-equations",
        "zero-curvature-condition" ;
    dcat:landingPage <https://hal.science/hal-00983782> .

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    dct:format "HTML" ;
    dct:issued "2026-05-05T12:22:47.786495"^^xsd:dateTime ;
    dct:modified "2026-05-05T12:22:47.765908"^^xsd:dateTime ;
    dct:title "Quasideterminant solutions of NC Painlevé II equation with the Toda solution at n= 1 as a seed solution in its Darboux transformation" ;
    dcat:accessURL <https://hal.science/hal-00983782> .

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