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), pp. 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 = {Loday-Richaud Mich\`ele},
     series = {Ast\'erisque},
     pages = {117--166},
     year = {2004},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {297},
     mrnumber = {2135677},
     zbl = {1086.34072},
     language = {en},
     url = {https://www.numdam.org/item/AST_2004__297__117_0/}
}
TY  - CHAP
AU  - Kawai, Takahiro
AU  - Koike, Tatsuya
AU  - Nishikawa, Yukihiro
AU  - Takei, Yoshitsugu
TI  - On the Stokes geometry of higher order Painlevé equations
BT  - Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II)
AU  - Collectif
ED  - Loday-Richaud Michèle
T3  - Astérisque
PY  - 2004
SP  - 117
EP  - 166
IS  - 297
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_2004__297__117_0/
LA  - en
ID  - AST_2004__297__117_0
ER  - 
%0 Book Section
%A Kawai, Takahiro
%A Koike, Tatsuya
%A Nishikawa, Yukihiro
%A Takei, Yoshitsugu
%T On the Stokes geometry of higher order Painlevé equations
%B Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II)
%A Collectif
%E Loday-Richaud Michèle
%S Astérisque
%D 2004
%P 117-166
%N 297
%I Société mathématique de France
%U https://www.numdam.org/item/AST_2004__297__117_0/
%G en
%F AST_2004__297__117_0
Kawai, Takahiro; Koike, Tatsuya; Nishikawa, Yukihiro; Takei, Yoshitsugu. On the Stokes geometry of higher order Painlevé equations, dans Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 117-166. https://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 | Zbl

[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 | Zbl

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

[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. | MR | Zbl | DOI

[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. | MR | Zbl | DOI

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

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

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

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

[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

[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. | MR | Zbl | DOI

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

[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 | Zbl

[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. | MR | Zbl | Numdam | EuDML

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

[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 | Zbl

[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. | MR | Zbl | EuDML | Numdam