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KIAM Preprint  13, Moscow, 2006
Authors: Bruno A. D., Goryuchkina I. V.
Expansions of Solutions to the Sixth Painlev'e Equation Near Singular Points x=0 x=∞.
Abstract:
We consider the sixth Painlev'e equation in the case a,b ≠ 0. By the methods of Power Geometry, near the singular points x=0 and x=∞, we have found all power, power-logarithmic and complicated expansions of its solutions. Near x=0 we have obtained 15 families of expansions, sixth of them are complicated. Using a symmetry of the equation, near x=∞ we have obtained again 15 families of expansions, including 6 complicated.
Publication language: russian
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