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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 068, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.068 (Mi sigma1367) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Numerical Approach to Painlevé Transcendents on Unbounded Domains

Christian Klein, Nikola Stoilov

Institut de Mathématiques de Bourgogne, UMR 5584, Université de Bourgogne-Franche-Comté, 9 avenue Alain Savary, 21078 Dijon Cedex, France
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DOI: https://doi.org/10.3842/SIGMA.2018.068
Abstract: A multidomain spectral approach for Painlevé transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a, possibly divergent, asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within said sector without the need of evaluating truncations of the series at any finite point. The accuracy of the method is illustrated for the example of the tritronquée solution to the Painlevé I equation.
Keywords: Painlevé equations; spectral methods.
Funding agency Grant number
Federación Española de Enfermedades Raras
Agence Nationale de la Recherche ANR-FWF
Marie Sklodowska-Curie Actions
This work was partially supported by the PARI and FEDER programs in 2016 and 2017, by the ANR-FWF project ANuI and by the Marie-Curie RISE network IPaDEGAN.
Received: April 18, 2018; in final form July 2, 2018; Published online July 12, 2018
Bibliographic databases:
Document Type: Article
MSC: 34M55; 65L10
Language: English
Citation: Christian Klein, Nikola Stoilov, “Numerical Approach to Painlevé Transcendents on Unbounded Domains”, SIGMA, 14 (2018), 068, 10 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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