On the Stokes geometry of higher order Painlevé equations
Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque no. 297  (2004), p. 117-166
@incollection{AST_2004__297__117_0,
     author = {Kawai, Takahiro and Koike, Tatsuya and Nishikawa, Yukihiro and Takei, Yoshitsugu},
     title = {On the Stokes geometry of higher order Painlev\'e equations},
     booktitle = {Analyse complexe, syst\`emes dynamiques, sommabilit\'e des s\'eries divergentes et th\'eories galoisiennes (II)},
     editor = {Loray-Richaud Mich\`ele},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {297},
     year = {2004},
     pages = {117-166},
     zbl = {1086.34072},
     mrnumber = {2135677},
     language = {en},
     url = {http://www.numdam.org/item/AST_2004__297__117_0}
}
Kawai, Takahiro; Koike, Tatsuya; Nishikawa, Yukihiro; Takei, Yoshitsugu. On the Stokes geometry of higher order Painlevé equations, in Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 117-166. http://www.numdam.org/item/AST_2004__297__117_0/

[AKT1] T. Aoki, T. Kawai & Y. Takei - "New turning points in the exact WKB analysis for higher order ordinary differential equations", in Analyse algébrique des perturbations singulières I; Méthodes résurgentes, Hermann, Paris, 1994, p. 69-84. | MR 1296472 | Zbl 0831.34058

[AKT2] T. Aoki, T. Kawai & Y. Takei, "WKB analysis of Painlevé transcendents with a large parameter II", in Structure of Solutions of Differential Equations, World Scientific, 1996, p. 1-49. | MR 1445330 | Zbl 0894.34050

[BNR] H. L. Berk, W. M. Nevins & K. V. Roberts - "New Stokes' line in WKB theory", J. Math. Phys. 23 (1982), p. 988-1002. | Article | MR 659998 | Zbl 0488.34050

[DT] E. Date & S. Tanaka - KdV Equation, Kinokuniya, Tokyo, 1979, in Japanese.

[FN] H. Flaschka & A. C. Newell - "Monodromy- and spectrum-preserving deformations I", Comm. Math. Phys. 76 (1980), p. 65-116. | Article | MR 588248 | Zbl 0439.34005

[GJP] P. R. Gordoa, N. Joshi & A. Pickering - "On a generalized 2 + 1 dispersive water wave hierarchy", Publ. RIMS, Kyoto Univ. 37 (2001), p. 327-347. | Article | MR 1855426 | Zbl 0997.35094

[GP] P. R. Gordoa & A. Pickering - "Nonisospectral scattering problems: A key to integrable hierarchies", J. Math. Phys. 40 (1999), p. 5749-5786. | Article | MR 1722336 | Zbl 1063.37544

[JM] M. Jimbo & T. Miwa - "Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II", Physica D 2 (1981), p. 407-448. | Article | MR 625446 | Zbl 1194.34166

[KT1] T. Kawai & Y. Takei - "WKB analysis of Painlevé transcendents with a large parameter I", Adv. in Math. 118 (1996), p. 1-33. | Article | MR 1375950 | Zbl 0848.34005

[KT2] T. Kawai & Y. Takei, "WKB analysis of Painlevé transcendents with a large parameter III", Adv. in Math. 134 (1998), p. 178-218. | Article | MR 1612399 | Zbl 0901.34057

[KT3] T. Kawai & Y. Takei, Algebraic Analysis of Singular Perturbations, Iwanami, Tokyo, 1998, in Japanese; an English translation is to be published by AMS. | MR 2182990

[KS] N. A. Kudryashov & M. B. Soukharev - "Uniformization and transcendence of solutions for the first and second Painlevé hierarchies", Phys. Lett. A 237 (1998), p. 206-216. | Article | MR 1609399 | Zbl 0941.34077

[L] P. D. Lax - "Almost periodic solutions of the KdV equation", SIAM Rev. 18 (1976), p. 351-375. | Article | MR 404889 | Zbl 0329.35015

[N1] Y. Nishikawa - "WKB analysis of PII-PIV hierarchies", Master thesis, Kyoto Univ., 2003, in Japanese.

[N2] Y. Nishikawa, "Towards the exact WKB analysis of PII-PIV hierarchies", in preparation.

[NT] Y. Nishikawa & Y. Takei - "On the structure of the Riemann surface in the Painlevé hierarchies", in preparation.

[O] K. Okamoto - "Isomonodromic deformation and Painlevé equations, and the Garnier systems", J. Fasc. Sci. Univ. Tokyo Sect. IA Math. 33 (1986), p. 575-618. | MR 866050 | Zbl 0631.34011

[S1] S. Shimomura - "Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29 (2000), no. 1, p. 1-17. | Numdam | MR 1765543 | Zbl 0952.35139

[S2] S. Shimomura, "On the Painlevé I hierarchy", RIMS Kôkyûroku 1203 (2001), p. 46-50. | MR 1854796 | Zbl 0985.34505

[T1] Y. Takei - "An explicit description of the connection formula for the first Painlevé equation", in Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear, Kyoto Univ. Press, 2000, p. 271-296. | MR 1770299 | Zbl 0989.34075

[T2] Y. Takei, "On a double turning point problem for systems of linear ordinary differential equations", preprint.

[V] A. Voros - "The return of the quartic oscillator. The complex WKB method", Ann. Inst. H. Poincaré. Phys. Théor. 39 (1983), p. 211-338. | Numdam | MR 729194 | Zbl 0526.34046