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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 3, Pages 515–526
DOI: https://doi.org/10.4213/tmf6369 (Mi tmf6369) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Padé approximations for Painlevé I and II transcendents

V. Yu. Novokshenov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (721 kB) Citations (24)
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DOI: https://doi.org/10.4213/tmf6369
Abstract: We use a version of the Fair–Luke algorithm to find the Padé approximate solutions of the Painlevé I and II equations. We find the distributions of poles for the well-known Ablowitz–Segur and Hastings–McLeod solutions of the Painlevé II equation. We show that the Boutroux tritronquée solution of the Painleé I equation has poles only in the critical sector of the complex plane. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behavior at infinity in the complex plane.
Keywords: Painlevé equation, meromorphic solution, distribution of poles, Padé approximation, continued fraction, Riemann–Hilbert problem.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 3, Pages 853–862
DOI: https://doi.org/10.1007/s11232-009-0073-8
Bibliographic databases:
Language: Russian
Citation: V. Yu. Novokshenov, “Padé approximations for Painlevé I and II transcendents”, TMF, 159:3 (2009), 515–526; Theoret. and Math. Phys., 159:3 (2009), 853–862
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v159/i3/p515
    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:78
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