Painlevé equations

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31: Bibliography

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Asymptotics of solutions of the generalized sine-Gordon equation, the third Painlevé equation and the d’Alembert equation. Dokl. Akad. Nauk SSSR 280 (2), pp. 265–268 (Russian).

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Notes:

English translation: Soviet Math. Dokl. 31(1985), no. 1, pp. 45–47

External Links:

ISSN 0002-3264, MathReview (M. S. Agranovich), ZentralBlatt

Referenced by:

§32.11(iv).

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Nonlinear chains and Painlevé equations. Phys. D 73 (4), pp. 335–351.

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ISSN 0167-2789, Document, MathReview (F. Pempinelli), ZentralBlatt

Referenced by:

§32.2(v).

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Rational solutions of Painlevé equations. Stud. Appl. Math. 61 (1), pp. 31–53.

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External Links:

ISSN 0022-2526, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§32.10(ii), §32.8(i), §32.8(v).

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Transformations $R{S}_4^2(3)$ of the ranks $\le 4$ and algebraic solutions of the sixth Painlevé equation. Comm. Math. Phys. 228 (1), pp. 151–176.

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ISSN 0010-3616, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

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32: Bibliography M

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Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of ${𝐏}^2$ . In Geometry of Differential Equations, A. Khovanskii, A. Varchenko, and V. Vassiliev (Eds.), Amer. Math. Soc. Transl. Ser. 2, Vol. 186, pp. 131–151.

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External Links:

MathReview (Bruce Hunt), ZentralBlatt

Referenced by:

§32.2(iv).

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Classical transcendental solutions of the Painlevé equations and their degeneration. Tohoku Math. J. (2) 56 (4), pp. 467–490.

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ISSN 0040-8735, Document, MathReview (Oleg Gleizer), ZentralBlatt

Referenced by:

§32.10(v), §32.10(vi).

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Bäcklund transformations and solution hierarchies for the third Painlevé equation. Stud. Appl. Math. 98 (2), pp. 139–194.

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External Links:

ISSN 0022-2526, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.10(iii), §32.7(iii), §32.8(iii), §32.9(i).

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Rational solutions of the second and the fourth Painlevé equations. Funkcial. Ekvac. 28 (1), pp. 1–32.

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

Referenced by:

§32.8(iv).

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Classical solutions of the third Painlevé equation. Nagoya Math. J. 139, pp. 37–65.

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

Referenced by:

§32.8(iii).

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33: Bibliography C

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The third Painlevé equation and associated special polynomials. J. Phys. A 36 (36), pp. 9507–9532.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§18.38(iii), §32.8(iii), §32.9(i).

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The fourth Painlevé equation and associated special polynomials. J. Math. Phys. 44 (11), pp. 5350–5374.

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ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§32.8(iv).

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Special polynomials associated with rational solutions of the fifth Painlevé equation. J. Comput. Appl. Math. 178 (1-2), pp. 111–129.

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ISSN 0377-0427, Document, MathReview (Davide Batic), ZentralBlatt

Referenced by:

§32.8(v), §32.9(ii).

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Painlevé Equations—Nonlinear Special Functions: Computation and Application. In Orthogonal Polynomials and Special Functions, F. Marcellàn and W. van Assche (Eds.), Lecture Notes in Math., Vol. 1883, pp. 331–411.

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External Links:

ISBN 3-540-31062-2, MathReview (Marta Mazzocco), ZentralBlatt

Referenced by:

Ch.32.

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Chazy’s second-degree Painlevé equations. J. Phys. A 39 (39), pp. 11955–11971.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§32.7(vii).

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34: Bibliography G

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Special classes of solutions of Painlevé equations. Differ. Uravn. 18 (3), pp. 419–429 (Russian).

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Notes:

In Russian. English translation: Differential Equations 18(3), pp. 317–326.

External Links:

ISSN 0374-0641, MathReview, ZentralBlatt

Referenced by:

§32.10(iv), §32.10(v), §32.8(iii), §32.8(v), §32.9(ii).

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Theory of Painlevé’s equations. Differ. Uravn. 11 (11), pp. 373–376 (Russian).

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Notes:

In Russian. English translation: Differential Equations 11(11), pp. 285–287

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.7(iii), §32.7(vi).

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One-parameter systems of solutions of Painlevé equations. Differ. Uravn. 14 (12), pp. 2131–2135 (Russian).

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Notes:

In Russian. English translation: Differential Equations 14(12), pp. 1510–1513 (1979)

External Links:

ISSN 0374-0641, MathReview (M. Tvrdý), ZentralBlatt

Referenced by:

§32.10(i), §32.10(ii), §32.10(iii), §32.7(iv).

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Theory of the fourth Painlevé equation. Differ. Uravn. 23 (5), pp. 760–768, 914 (Russian).

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Notes:

In Russian. English translation: Differential Equations 23(5), pp. 506–513

External Links:

ISSN 0374-0641, MathReview (C. S. Coleman), ZentralBlatt

Referenced by:

§32.10(iv), §32.7(iv), §32.8(iv).

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Painlevé Differential Equations in the Complex Plane. Studies in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin-New York.

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External Links:

ISBN 3-11-017379-4, MathReview, ZentralBlatt

Referenced by:

§32.10(i), §32.10(iii), §32.10(iv), §32.10(v), §32.10(vi), §32.2(iv), §32.7(iii), §32.7(iv), §32.7(v), §32.7(vi), §32.7(vii), §32.8(ii), §32.8(iii), §32.8(iv), §32.8(v), §32.9(i), §32.9(ii), §32.9(iii).

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35: Bibliography V

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On the rational solutions of the second Painlevé equation. Differ. Uravn. 1 (1), pp. 79–81 (Russian).

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Notes:

In Russian. English translation: Differential Equations 1(1), pp. 58–59.

External Links:

MathReview, ZentralBlatt

Referenced by:

§32.8(ii).

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36: Bibliography B

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Integral equations and exact solutions for the fourth Painlevé equation. Proc. Roy. Soc. London Ser. A 437, pp. 1–24.

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External Links:

ISSN 0962-8444, FullText, MathReview (Mehmet Can), ZentralBlatt

Referenced by:

§32.11(v), §32.2(iii).

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Numerical studies of the fourth Painlevé equation. IMA J. Appl. Math. 50 (2), pp. 167–193.

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External Links:

ISSN 0272-4960, Document, MathReview, ZentralBlatt

Referenced by:

§32.17, §32.3(iii).

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Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Stud. Appl. Math. 95 (1), pp. 1–71.

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External Links:

ISSN 0022-2526, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.10(iv), §32.2(iii), §32.7(iv), §32.8(iv).

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The Painlevé III equation and the Iwasawa decomposition. Manuscripta Math. 87 (3), pp. 369–377.

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External Links:

ISSN 0025-2611, Document, MathReview (J. Dorfmeister), ZentralBlatt

Referenced by:

§32.11(iv).

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Recherches sur les transcendantes de M. Painlevé et l’étude asymptotique des équations différentielles du second ordre. Ann. Sci. École Norm. Sup. (3) 30, pp. 255–375.

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External Links:

ISSN 0012-9593, MathReview Entry, ZentralBlatt

Referenced by:

§32.12(i), §32.12(ii).

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37: Bibliography T

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On the connection formula for the first Painlevé equation—from the viewpoint of the exact WKB analysis. Sūrikaisekikenkyūsho Kōkyūroku (931), pp. 70–99.

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Notes:

Painlevé functions and asymptotic analysis (Japanese) (Kyoto, 1995)

External Links:

FullText, MathReview (Andrei A. Kapaev)

Referenced by:

§32.12(i).

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38: Bibliography H

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A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

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External Links:

ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

Referenced by:

§32.11(ii).

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Poncelet Polygons and the Painlevé Equations. In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.), pp. 151–185.

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External Links:

MathReview (Henrik Pedersen), ZentralBlatt

Referenced by:

§32.9(iii).

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39: Bibliography W

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Solutions of the fifth Painlevé equation. I. Hokkaido Math. J. 24 (2), pp. 231–267.

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External Links:

ISSN 0385-4035, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.10(v).

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40: Bibliography S

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Rational surfaces associated with affine root systems and geometry of the Painlevé equations. Comm. Math. Phys. 220 (1), pp. 165–229.

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External Links:

ISSN 0010-3616, Document, MathReview (I. Dolgachev), ZentralBlatt

Referenced by:

§32.7(viii).

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Asymptotic solutions of nonlinear evolution equations and a Painlevé transcendent. Phys. D 3 (1-2), pp. 165–184.

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External Links:

Document, ZentralBlatt

Referenced by:

§32.11(ii).

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The relation between asymptotic properties of the second Painlevé equation in different directions towards infinity. Differ. Uravn. 23 (5), pp. 834–842 (Russian).

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Notes:

In Russian. English translation: Differential Equations 23(1987), no. 5, pp. 569–576.

External Links:

ISSN 0374-0641, MathReview (T. Chanturiya), ZentralBlatt

Referenced by:

§32.11(ii).

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