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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf6369https://doi.org/10.4213/tmf6369 https://www.mathnet.ru/eng/tmf/v159/i3/p515
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Abstract page: | 589 | Full-text PDF : | 232 | References: | 65 | First page: | 24 |
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