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Preprints of the Keldysh Institute of Applied Mathematics, 2008, 075, 30 pp. (Mi ipmp427)  

All expansions of solutions to the sixth Painlevé equation near its nonsingular point

A. D. Bruno, I. V. Goryuchkina
References:
Abstract: Here we consider the sixth Painlevé equation for all values of four its complex parameters $a,b,c,d$ near its nonsingular point $x=x_0\ne 0,1,\infty$ 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 Painlevé equation. Eight of these 17 families are new. The other 9 families were known.
Document Type: Preprint
Language: Russian
Citation: A. D. Bruno, I. V. Goryuchkina, “All expansions of solutions to the sixth Painlevé equation near its nonsingular point”, Keldysh Institute preprints, 2008, 075, 30 pp.
Citation in format AMSBIB
\Bibitem{BruGor08}
\by A.~D.~Bruno, I.~V.~Goryuchkina
\paper All expansions of solutions to the sixth Painlev\'e equation near its nonsingular point
\jour Keldysh Institute preprints
\yr 2008
\papernumber 075
\totalpages 30
\mathnet{http://mi.mathnet.ru/ipmp427}
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    Препринты Института прикладной математики им. М. В. Келдыша РАН
     
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