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Preprints of the Keldysh Institute of Applied Mathematics, 2006, 002, 30 pp. (Mi ipmp550)  

Expansions of solutions to the sixth painleve equation in cases $a=0$ and $b=0$

A. D. Bruno, I. V. Goryuchkina
Abstract: We consider the sixth Painleve equation for $a=0$. For the case we obtain six new expansions of solutions for $x\to0$ and $x\to\infty$. They are different from expansions known for $a\ne0$ and found early (Doklady Mathematics, 2004, v. 69, no. 2). Among six new expansions, four are power expansions, and two are complicated ones, i.e., they have nonpower asymptotics. Except that, we obtain new expansions of solutions for $b=0$. We use for this symmetry of the equation. All found here expansions are new.
Document Type: Preprint
Language: Russian
Citation: A. D. Bruno, I. V. Goryuchkina, “Expansions of solutions to the sixth painleve equation in cases $a=0$ and $b=0$”, Keldysh Institute preprints, 2006, 002, 30 pp.
Citation in format AMSBIB
\Bibitem{BruGor06}
\by A.~D.~Bruno, I.~V.~Goryuchkina
\paper Expansions of solutions to the sixth painleve equation in cases $a=0$ and $b=0$
\jour Keldysh Institute preprints
\yr 2006
\papernumber 002
\totalpages 30
\mathnet{http://mi.mathnet.ru/ipmp550}
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    Препринты Института прикладной математики им. М. В. Келдыша РАН
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