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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions

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Lettere al Nuovo Cimento (1971-1985)

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References

  1. P. Painlevé:Bull. Soc. Math. Fr.,28, 214 (1900)

    Google Scholar 

  2. P. Painlevè:Acta Math.,25, 1 (1902).

    Article  MathSciNet  Google Scholar 

  3. B. Gambier:Acta Math.,33, 1 (1909).

    Article  MathSciNet  Google Scholar 

  4. E. L. Ince:Ordinary Differential Equations (New York, N. Y., 1947).

  5. E. Barouch, B. M. McCoy andT. T. Wu:Phys. Rev. Lett.,31, 1409 (1973).

    Article  ADS  Google Scholar 

  6. M. Jimbo,T. Miwa,Y. Mori andM. Sato:Physica D (The Hague), ID, No. 1, 80 (1980).

  7. J. W. Miles:On cumulative nonlinearity for a weakly dispersive gravity wave (preprint).

  8. M. J. Ablowitz andH. Segue:Phys. Rev. Lett.,38, 1103 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  9. M. J. Ablowitz, A. Ramani andH. Segur:Lett. Nuovo Cimento,23, 333 (1978)

    Article  MathSciNet  Google Scholar 

  10. M. J. Ablowitz, A. Ramani andH. Segue:J. Math. Phys. (N. Y.),21, 715 (1980)

    Article  ADS  Google Scholar 

  11. M. J. Ablowitz, A. Ramani andH. Segur:J. Math. Phys. (N. Y.),21, 1006 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  12. C. Gardner, J. M. Green, M. D. Kruskal andR. M. Miura:Phys. Rev. Lett.,19, 1095 (1967)

    Article  ADS  Google Scholar 

  13. H. Flaschka andA. C. Newell:Monodromy preserving deformations, preprint (1979).

  14. M. Sato, T. Miwa andM. Jimbo: a series of papers entitledHolonomic Quantum Fields:Publ. RIMS, Kyoto Univ.,14, 223 (1977)

    Article  MathSciNet  Google Scholar 

  15. M. Sato, T. Miwa andM. Jimbo: a series of papers entitledHolonomic Quantum Fields:Publ. RIMS, Kyoto Univ.,15, 201 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  16. M. Sato, T. Miwa andM. Jimbo: a series of papers entitledHolonomic Quantum Fields:Publ. RIMS, Kyoto Univ.,15, 871 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  17. K. Ueno :Monodromy preserving deformations of linear differential equations with irregular singular points, RIMS preprint 301 (1979).

  18. M. Jimbo andT. Miwa:Deformations of linear ODE, RIMS preprint 315 (1980)

  19. M. Jimbo andT. Miwa:Monodromy preserving deformation of linear ODEs with rational coefficients, RIMS preprint, 327 (1980)

  20. M. Jimbo andT. Miwa:Deformation of linear ODEs, RIMS preprint 329 (1980).

  21. H. Airaut:Stud. Appl. Math.,61. 31 (1979).

    MathSciNet  ADS  Google Scholar 

  22. M. Boiti andF. Pempinelli:Nuovo Cimento B,51, 70 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  23. M. Boiti andF. Pempinelli: preprint (1980).

  24. N. A. Lukashevich:Diff. Urav.,7, No. 1, 1124 (1971).

    MATH  Google Scholar 

  25. V. I. Gromak:Diff. Urav.,11, No. 2, 373 (1975).

    MathSciNet  MATH  Google Scholar 

  26. N. A. Lukashevich:Author’s Abstract of Doctoral Dissertation (in Russian (Kiev, 1971).

  27. V. I. Gromak:Diff. Urav.,12, No. 4, 740 (1976).

    MathSciNet  Google Scholar 

  28. N. P. Erugin:Diff. Urav.,12, No. 3, 387 (1976)

    MathSciNet  MATH  Google Scholar 

  29. N. P. Erugin:Diff. Urav.,12, No. 4, 579 (1976).

    MathSciNet  Google Scholar 

  30. V. I. Gromak:Diff. Urav.,14, No. 12, 2131 (1978).

    MathSciNet  Google Scholar 

  31. N. P. Erugin:Dokl. Akad. Nauk. BSSR,2, No. 4 (1958).

  32. N. A. Lukashevich:Diff. Urav.,3, No. 11, 994 (1967).

    MATH  Google Scholar 

  33. N. A. Lukashevich:Diff. Urav.,3, No. 5, 395 (1967).

    MathSciNet  MATH  Google Scholar 

  34. N. A. Lukashevich:Diff. Urav.,4, No. 8, 732 (1968).

    Google Scholar 

  35. N. A. Lukashevich andA. I. Yablonskii:Diff. Urav.,3, No. 3, 264 (1967).

    Google Scholar 

  36. Fuchs:Sitz. Akad. Wiss. Berlin,32, 669 (1884).

    Google Scholar 

  37. A. S. Fokas andM. J. Ablowitz: in preparation.

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Authors and Affiliations

  1. Mathematics and Computer Science, Clarkson College, 13676, Potsdam, New York

    A. S. Pokas

  2. Departments of Chemical and Petroleum Engineering, University of Southern California, 90007, Los Angeles, Cal.

    Y. C. Tortsos

Authors
  1. A. S. Pokas
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  2. Y. C. Tortsos
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Pokas, A.S., Tortsos, Y.C. The transformation properties of the sixth Painlevé equation and one-parameter families of solutions. Lett. Nuovo Cimento 30, 539–544 (1981). https://doi.org/10.1007/BF02739686

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