Advertisement

Transseries And Formal Integral For The First Painlevé Equation

  • Eric Delabaere
Chapter
  • 799 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2155)

Abstract

Abstract This chapter has two purposes. Our first goal is to construct the socalled “formal transseries solutions” for the prepared form associated with the first Painlevé equation, which will be used later on to get the truncated solutions : this is done in Sect. 5.3, after some preliminaries in Sect. 5.1 and Sect. 5.2. Our second goal is to build the formal integral for the first Painlevé equation and, equivalently, the canonical normal form equation to which the first Painlevé equation is formally conjugated. This is what we do in Sect. 5.4. These informations will be used in a next chapter to investigate the resurgent structure for the first Painlevé equation.

Keywords

Formal Solution Formal Integral Formal Series Linear Differential Operator Newton Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Eric Delabaere
    • 1
  1. 1.Département de MathématiquesUniversité d’AngersAngersFrance

Personalised recommendations