Abstract
This chapter is devoted to the construction of the tritruncated solutions for the first Painlevé equation, the existence of which being announced in Sect. 2.6. This example will introduce the reader to common reasonings in resurgence theory. We construct a prepared form associated with the first Painlevé equation (Sec 3.1). This prepared ODE has a unique formal solution from which we deduce the existence of truncated solutions by application of the “‘main asymptotic existence theorem”. We then study the Borel-Laplace summability property of the formal solution by various methods (Sect. 3.3). One deduces the existence of the tritruncated solutions for the first Painlevé equation, by Borel-Laplace summation (Sect. 3.4).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Delabaere, E. (2016). Tritruncated Solutions For The First Painlevé Equation. In: Divergent Series, Summability and Resurgence III. Lecture Notes in Mathematics, vol 2155. Springer, Cham. https://doi.org/10.1007/978-3-319-29000-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-29000-3_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28999-1
Online ISBN: 978-3-319-29000-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)