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KIAM Preprint № 75, Moscow, 2008
Authors: Bruno A. D., Goryuchkina I. V.
All Expansions of Solutions to the Sixth Painlev'e Equation Near Its Nonsingular Point
Abstract:
Here we consider the sixth Painlev'e equation for all values of four its complex parameters a,b,c,d near its nonsingular point x = x0 ≠ 0,1,∞ and we look for all asymptotic expansions of its solutions of four types: power, power-logarithmic, complicated, exotic and also exponential asymptotic forms. Altogether they form 17 families and all of them are power. Expansions of other three types and exponent asymptotic forms are absent, as it must be for a Painlev'e equation. Eight of these 17 families are new. The other 9 families were known.
Publication language: russian,  pages: 30
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bruno Alexander Dmitrievich,  orcid.org/0000-0002-7465-1258KIAM RAS
  • Goryuchkina I. V.,  KIAM RAS