Geodesic
Asymptotic expressions for the second Painlevй functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 3, pp. 323-332 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of isomonodromicJdeformations is used to investigate the asymptotic properties of solutions of the second Painlevé equation (I). The leading terms as $x\to\pm\infty$ of the second Painlevé functions are constructed for the general case. The parameters of the asymptotic behavior are expressed in terms of first inteErals of the Painlevé equation, which are the monodromy data of the associated system (2) of linear ordinary differential equations with rational coefficients. The asymptotic behaviors of the real and imaginary second Painlevé functions are separated. 
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     author = {A. A. Kapaev},
     title = {Asymptotic expressions for the second {Painlev{\cyrishrt}} functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--332},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_3_a0/}
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A. A. Kapaev. Asymptotic expressions for the second Painlevй functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 3, pp. 323-332. http://geodesic.mathdoc.fr/item/TMF_1988_77_3_a0/

[1] Ablowitz M., Segur H., Stud. Appl. Math., 57 (1977), 13–44 | DOI | MR | Zbl

[2] Smith R., J. Fluid Mech., 77 (1976), 417–431 | DOI | MR | Zbl

[3] Zakharov V. E., Kuznetsov E. A., ZhETF, 91:4(10) (1986), 1310–1324

[4] Novokshenov V. Yu., Diff. uravneniya, 21:11 (1985), 1915 | MR | Zbl

[5] Ablowitz M., Ramani A., Segur H., J. Math. Phys., 21:4 (1980), 715–721 ; 5, 1006–1015 | DOI | MR | Zbl | MR | Zbl

[6] Flaschka H., Newell A. C., Commun. Math. Phys., 76:1 (1980), 65–116 | DOI | MR | Zbl

[7] Umbo M., Miwa T., Physica D, 2 (1981), 407–448 | DOI | MR

[8] Its A. R., Izv. AN SSSR, ser. matem., 49:3 (1985), 530–565 | MR | Zbl

[9] Novokshenov V. Yu., Funkts. analiz i ego prilozh., 18:3 (1984), 90–91 | MR | Zbl

[10] Its A. R., Novokshonov V. Yu., “The isomonodromic deformation method in the theorie of Painlevé equations”, Lecture notes in mathematics, 1191, Springer-Verlag, Berlin–Heidelberg–New York–Tokio, 1986 | DOI | MR | Zbl

[11] Kapaev A. A., Novokshenov V. Yu., DAN SSSR, 290:3 (1986), 590–594 | MR | Zbl

[12] Novokshenov V. Yu., Suleimanov B. I., UMN, 39:4 (1984), 114–115

[13] Yablonskii A. I., Vestsi AN BSSR. ser. fiz.-tekhn. navuk, 1959, no. 3, 30–35

[14] Vorobev A. P., Diff. uravneniya, 1:1 (1965), 79–81 | MR

[15] Lukashevich N. A., Diff. uravneniya, 7:6 (1971), 1124–1125 | MR | Zbl

[16] Erugin N. P., DAN BSSR, 2:4 (1958), 139–142 | MR

[17] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | MR | Zbl

[18] Haberman R., Stud. Appl. Math., 57 (1977), 247–270 | DOI | MR | Zbl

[19] Abdullaev A. S., DAN SSSR, 273:5 (1983), 1033–1036 ; Дифф. уравнения, 23:3 (1987), 509 | MR | Zbl | Zbl

[20] Its A. R., Kapaev A. A., Izv. AN SSSR, ser. matem., 51:4 (1987), 878–892 | MR | Zbl

[21] Boutroux P., Ann. Sci. l'Ecole Norm. Super., 30 (1913), 255–376 ; 31 (1914), 99–159 | DOI | MR | DOI | MR | Zbl

[22] McCoy B. M., Thang Sh., Physica D, 19 (1986), 42–72 ; 20, 187–216 | DOI | MR | Zbl | DOI | MR | Zbl