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Studies on the Painlevé equations

III. Second and fourth painlevé equations,P II andP IV

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References

  1. Airault, H.: Rational solutions of Painlevé equations. Studies in Appl. Math.61, 31–53 (1979)

    Google Scholar 

  2. Bourbaki, N.: Groupes et algèbres de Lie. Chaps. 4–6. Paris: Masson 1980

    Google Scholar 

  3. Bureau, F.J.: Les équations différentielles du second ordre à points critiques fixes, I. Les intégrales de l'équation A2 de Painlevé. Bull. Cl. Sci. Acad. Roy. Belg.69, 80–104 (1983); II. Les intégrales de l'équation A4 de Painlevé, ibid Bull. Cl. Sci. Acad. Roy. Belg.69 397–433 (1983)

    Google Scholar 

  4. Darboux, G.: Leçons sur la théorie générale des surfaces. tII. 137. Chelsea 1972

  5. Jimbo, M., Miwa, T.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients, II. Physica2 D, 407–448 (1981)

    Google Scholar 

  6. Kametaka, Y.: On poles of the rational solution of the Toda equation of Painlevé-II type. Proc. Japan Acad. Ser. A59, 358–360 (1983)

    Google Scholar 

  7. Kametaka, Y.: On poles of the rational solution of the Toda equation of Painlevé-IV type. Proc. Japan Acad. Ser. A59, 453–455 (1983)

    Google Scholar 

  8. Lukashevich, N.A.: Theory of the fourth Painlevé equation. Diffeer. Uravn.3, 395–399 (1967)

    Google Scholar 

  9. Lukashevich, N.A.: The second Painlevé equation. Differ. Uravn.7, 853–854 (1971)

    Google Scholar 

  10. Murata, Y.: Rational solutions of the second and the fourth Painlevé equations. Funkc. Ekvacioy. Ser. Int.28, 1–32 (1985)

    Google Scholar 

  11. Okamoto, K.: Sur les feuilletages associés aux équations du second ordre à points critiques fixes de P. Painlevé. Jap. J. Math.5, 1–79 (1979)

    Google Scholar 

  12. Okamoto, K.: Polynomial Hamiltonians associated with Painlevé equations, I. Proc. Japan Acad. Ser. A56, 264–268 (1980); II, ibid. Proc. Japan Acad. Ser. A56 367–371 (1980)

    Google Scholar 

  13. Okamoto, K.: On the τ-function of the Painlevé equations. Physica2 D, 525–535 (1981)

    Google Scholar 

  14. Okamoto, K.: Studies on the Painlevé equations I, sixth Painlevé equationP VI. Ann. Mat.; II, fifth Painlevé equationP v. Jap. J. Math. 1986

  15. Okamoto, K.: Sur les échelles associées aux fonctions spéciales et léquation de Toda, preprint 1985

  16. Vorob'ev, A.P.: On rational solutions of the second Painlevé equation. Differ. Uravn.1, 58–59 (1965)

    Google Scholar 

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Address after September 20, 1986: Department of Mathematics, University of Tokyo, Komaba, Meguro, Tokyo, Japan

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Okamoto, K. Studies on the Painlevé equations. Math. Ann. 275, 221–255 (1986). https://doi.org/10.1007/BF01458459

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