On the Darboux integrability of the Painlevé II equations

In this paper we prove the non-existence of Darboux first integrals for the Painlev' II equations x = y - z/2- x2 , y = α + 1/2 + 2xy, z = 1 for all values of α ∈ C \ {αn : n = 2, 4, . . .}. These αn are real and larger than -1/2.

Bibliographic Details
Authors: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Format: article
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:145372
Online Access:https://ddd.uab.cat/record/145372
https://dx.doi.org/urn:doi:10.1080/14029251.2015.996441
Access Level:Open access
Keyword:Darboux integrability
Hamiltonian system
Painleve transcendents
Description
Summary:In this paper we prove the non-existence of Darboux first integrals for the Painlev' II equations x = y - z/2- x2 , y = α + 1/2 + 2xy, z = 1 for all values of α ∈ C \ {αn : n = 2, 4, . . .}. These αn are real and larger than -1/2.