Painlevé equations

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11: Bibliography Q

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A note on an open problem about the first Painlevé equation. Acta Math. Appl. Sin. Engl. Ser. 24 (2), pp. 203–210.

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External Links:

ISSN 0168-9673, Document, MathReview (Dmitrii Petrovich Novikov), ZentralBlatt

Referenced by:

§32.11(i).

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12: 32.3 Graphics

§32.3 Graphics

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§32.3(i) First Painlevé Equation

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§32.3(ii) Second Painlevé Equation with $\alpha =0$

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§32.3(iii) Fourth Painlevé Equation with $\beta =0$

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Figure 32.3.10: $u_k(x;\frac{5}{2})$ for $-12\le x\le 4$ with $k=\mathrm{0.24499\hspace{0.33em}2}$, $\mathrm{0.24499\hspace{0.33em}3}$. … Magnify

13: Bibliography U

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Solutions of the third Painlevé equation. I. Nagoya Math. J. 151, pp. 1–24.

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External Links:

ISSN 0027-7630, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.10(iii).

Encodings:

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On the transformation group of the second Painlevé equation. Nagoya Math. J. 157, pp. 15–46.

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External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.7(viii).

Encodings:

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14: Peter A. Clarkson

… ►Clarkson has published numerous papers on integrable systems (primarily Painlevé equations), special functions, and symmetry methods for differential equations. …

15: Alexander I. Bobenko

… ► Matveev), published by Springer in 1994, Painlevé Equations in the Differential Geometry of Surfaces (with U. …

16: Bibliography O

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On the $\tau$-function of the Painlevé equations. Phys. D 2 (3), pp. 525–535.

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External Links:

ISSN 0167-2789, Document, MathReview (D. A. Lutz), ZentralBlatt

Referenced by:

§32.6(i), §32.6(ii).

Encodings:

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Studies on the Painlevé equations. III. Second and fourth Painlevé equations, $P_{\mathrm{II}}$ and $P_{\mathrm{IV}}$ . Math. Ann. 275 (2), pp. 221–255.

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External Links:

ISSN 0025-5831, Document, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.10(ii), §32.10(iv), §32.6(iii), §32.6(v), §32.7(viii).

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Studies on the Painlevé equations. I. Sixth Painlevé equation $P_{\mathrm{VI}}$ . Ann. Mat. Pura Appl. (4) 146, pp. 337–381.

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External Links:

ISSN 0003-4622, Document, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.10(vi), §32.6(v), §32.7(vii), §32.7(viii).

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Studies on the Painlevé equations. II. Fifth Painlevé equation $P_{\mathrm{V}}$ . Japan. J. Math. (N.S.) 13 (1), pp. 47–76.

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External Links:

ISSN 0289-2316, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.10(v), §32.6(v), §32.7(viii).

Encodings:

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Studies on the Painlevé equations. IV. Third Painlevé equation $P_{\mathrm{III}}$ . Funkcial. Ekvac. 30 (2-3), pp. 305–332.

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External Links:

ISSN 0532-8721, FullText, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.10(iii), §32.2(iii), §32.6(iv), §32.7(viii).

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17: 32.2 Differential Equations

… ►The six Painlevé equations ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ are as follows: … ►

§32.2(ii) Renormalizations

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§32.2(iii) Alternative Forms

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§32.2(iv) Elliptic Form

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18: 32.9 Other Elementary Solutions

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§32.9(i) Third Painlevé Equation

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§32.9(ii) Fifth Painlevé Equation

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§32.9(iii) Sixth Painlevé Equation

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19: 32.8 Rational Solutions

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§32.8(ii) Second Painlevé Equation

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§32.8(iii) Third Painlevé Equation

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§32.8(iv) Fourth Painlevé Equation

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§32.8(v) Fifth Painlevé Equation

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20: Bibliography N

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Affine Weyl groups, discrete dynamical systems and Painlevé equations. Comm. Math. Phys. 199 (2), pp. 281–295.

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External Links:

ISSN 0010-3616, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.2(v).

Encodings:

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Symmetries in the fourth Painlevé equation and Okamoto polynomials. Nagoya Math. J. 153, pp. 53–86.

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External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.8(iv).

Encodings:

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Painlevé Equations through Symmetry. Translations of Mathematical Monographs, Vol. 223, American Mathematical Society, Providence, RI.

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Notes:

Translated from the 2000 Japanese original by the author

External Links:

ISBN 0-8218-3221-2, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.2(v).

Encodings:

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The asymptotic behavior of the general real solution of the third Painlevé equation. Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).

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Notes:

In Russian. English translation: Sov. Math., Dokl. 30(1988), no. 8, pp. 666–668.

External Links:

ISSN 0002-3264, MathReview (Vojislav Marić), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

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The Boutroux ansatz for the second Painlevé equation in the complex domain. Izv. Akad. Nauk SSSR Ser. Mat. 54 (6), pp. 1229–1251 (Russian).

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Notes:

In Russian. English translation: Math. USSR-Izv. 37(1991), no. 3, pp. 587–609.

External Links:

ISSN 0373-2436, Document, MathReview (Alexander I. Bobenko), ZentralBlatt

Referenced by:

§32.12(ii).

Encodings:

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