A unified approach to the Painleve Transcendents

2016/01/15 by Norbert Steinmetz, Steinmetz, Norbert
Mathematics · #30D35 #30D45 #34M05 #34M55 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30D35 #msc:30D45 #msc:34M05 #msc:34M55

paper · pdf · doi:10.48550/arxiv.1601.04031

34 pages

arxiv created 2016/01/15 · arxiv updated 2016/01/18

Abstract

We utilise a recent approach via the so-called re-scaling method to derive a unified and comprehensive theory of the solutions to Painleve's differential equations (I), (II) and (IV), with emphasis on the most elaborate equation (IV).

Related

• Classical transcendental solutions of the Painlevé equations and their degeneration
• Painlevé II transcendents and their squares
• Painlevé equations and the middle convolution
• The Painlevé transcendents with solvable monodromy
• Painlevé IV and a third-order viewpoint