New simple exact solutions to equation \(P_6\). (English) Zbl 1291.34152
Bruno, Alexander D. (ed.) et al., Painlevé equations and related topics. Proceedings of the international conference, Saint Petersburg, Russia, June 17–23, 2011. Berlin: de Gruyter (ISBN 978-3-11-027558-2/hbk; 978-3-11-027566-7/ebook). De Gruyter Proceedings in Mathematics, 13-21 (2012).
Summary: We compute exact solutions to the sixth Painlevé equation \((P_6)\) in the form of finite sums of power functions with rational power exponents. Our method essentially uses algorithms of power geometry for computing power expansions of solutions to an ordinary differential equation and computer algebra. New exact solutions are obtained.
For the entire collection see [Zbl 1248.34002].
For the entire collection see [Zbl 1248.34002].
MSC:
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
