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On the asymptotics of the real solutions to the general sixth Painlevé equation

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  • Huizeng Qin
  • Youmin Lu

Abstract

We study the general sixth Painlevé equation, develop, and justify the existence of several groups of asymptotics of its real solutions. Our methods also justify the differentiability of the asymptotics. Particular attention is paid to the solutions between 0 and 1. We find the asymptotics of all real solutions between 0 and 1 of the sixth Painlevé equation as x → + ∞ .

Suggested Citation

  • Huizeng Qin & Youmin Lu, 2006. "On the asymptotics of the real solutions to the general sixth Painlevé equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-10, November.
    • Handle: RePEc:hin:jijmms:069562
    DOI: 10.1155/IJMMS/2006/69562
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