Tronquée Solutions of the Third and Fourth Painlevé Equations

2018/03/31 by Xiaoyue Xia
Computer Science · Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Mathematical physics #Mathematics #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Pure mathematics #math.CA

paper · pdf · doi:10.3842/sigma.2018.095

published as SIGMA 14 (2018), 095, 28 pages

arxiv created 2018/09/08 · openalex publication_date 2018/09/08 · arxiv updated 2018/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recently in a paper by Lin, Dai and Tibboel, it was shown that the third and fourth Painlev equations have tronque and tritronque solutions. We obtain global information about these tronque and tritronque solutions. We find their sectors of analyticity, their Borel summed representations in these sectors as well as the asymptotic position of the singularities near the boundaries of the analyticity sectors. We also correct slight errors in the paper mentioned.

Citations

• On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations
• Quasi-linear Stokes phenomenon for the second Painlev transcendent
• On the formation of singularities of solutions of nonlinear differential systems in antistokes directions
• Location of Poles for the Hastings-McLeod Solution to the Second Painlevé Equation
• Painlevé Equations — Nonlinear Special Functions