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Asymptotic expressions for the second Painlevé functions

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Literature Cited

  1. M. Ablowitz and H. Segur, Stud. Appl. Math.,57, 13 (1977).

    Google Scholar 

  2. R. Smith, J. Fluid Mech.,77, 417 (1976).

    Google Scholar 

  3. V. E. Zakharov and E. A. Kuznetsov, Zh. Eksp. Teor. Fiz.,91, 1310 (1986).

    Google Scholar 

  4. V. Yu. Novokshenov, Diff. Equations,21, 1915 (1985).

    Google Scholar 

  5. M. Ablowitz, A. Ramani, and H. Segur, J. Math. Phys.,21, 715, 1006 (1980).

    Google Scholar 

  6. H. Flaschka and A. C. Newell, Commun. Math. Phys.,76, 65 (1980).

    Google Scholar 

  7. M. Jimbo and T. Miwa, Physica (Utrecht) D,2, 407 (1981).

    Google Scholar 

  8. A. R. Its, Izv. Akad. Nauk SSSR, Ser. Mat.,49, 530 (1985).

    Google Scholar 

  9. V. Yu. Novokshenov, Funktsional. Analiz i Ego Prilozhen.,18, 90 (1984).

    Google Scholar 

  10. A. R. Its and V. Yu. Novokshenov, The Isomonodromic Deformation Method in the Theory of Painlevé Equations, in: Lecture Notes in Mathematics, Vol. 1191, Springer Verlag, Berlin (1986).

    Google Scholar 

  11. A. A. Kapaev and V. Yu. Novokshenov, Dokl. Akad. Nauk SSSR,290, 590 (1986). A. A. Kapaev, Singular Solutions of the Painlevé II Equation, in: Lecture Notes in Mathematics, Vol. 1191, Springer Verlag, Berlin (1986), p. 261.

    Google Scholar 

  12. V. Yu. Novokshenov and B. I. Suleimanov, Usp. Mat. Nauk,39, 114 (1984).

    Google Scholar 

  13. A. I. Yablonskii, Vestsi Akad. Navuk B. SSR Ser. Fiz. Tekhm. Navuk, No. 3, 30 (1959).

    Google Scholar 

  14. A. P. Vorob'ev, Diff. Equations,1, 79 (1965).

    Google Scholar 

  15. N. A. Lukashevich, Diff. Equations,7, 1124 (1971).

    Google Scholar 

  16. N. P. Erugin, Dokl. Akad. Nauk B. SSR,2, 139 (1958).

    Google Scholar 

  17. M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  18. R. Haberman, Stud. Appl. Math.,57, 247 (1977).

    Google Scholar 

  19. A. S. Abdullaev, Dokl. Akad. Nauk SSSR,273, 1033 (1983); Diff. Equations,23, 509 (1987).

    Google Scholar 

  20. A. R. Its and A. A. Kapaev, Izv. Akad. Nauk SSSR Ser. Mat.,51, 878 (1987).

    Google Scholar 

  21. P. Boutroux, Ann. Sci. l'Ecole Norm. Super.,30, 255 (1913);31, 99 (1914).

    Google Scholar 

  22. B. M. McCoy and Sh. Thang, Physica (Utrecht) D,19, 42 (1986);20, 187 (1986).

    Google Scholar 

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Authors
  1. A. A. Kapaev
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Institute of Aircraft Instrument Construction, Leningrad. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 77, No. 3, pp. 323–332, December, 1988.

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Kapaev, A.A. Asymptotic expressions for the second Painlevé functions. Theor Math Phys 77, 1227–1234 (1988). https://doi.org/10.1007/BF01016976

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