Journal of Nonlinear Mathematical Physics

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Volume 22, Issue 1, December 2014, Pages 60 - 75

On the Darboux integrability of the Painlevé II equations

Authors
Jaume Llibre
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain.jllibre@mat.uab.cat
Claudia Valls
Departamento de Matemática, Instituto Superior Técnico, 1049–001 Lisboa, Portugal.cvalls@math.ist.utl.pt
Received 10 July 2014, Accepted 26 September 2014, Available Online 6 January 2021.
DOI
10.1080/14029251.2015.996441How to use a DOI?
Keywords
Painleve transcendents; Hamiltonian systems; Darboux integrability
Abstract

In this paper we prove the non–existence of Darboux first integrals for the Painlevé II equations

x.=y−z2−x2,y.=α+12+2xy,ż=1
for all values of α ∊ ℂ \ {αn: n = 2,4,…}. These αn are real and larger than −1/2.

Copyright
© 2015 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
22 - 1
Pages
60 - 75
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2015.996441How to use a DOI?
Copyright
© 2015 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Jaume Llibre
AU  - Claudia Valls
PY  - 2021
DA  - 2021/01/06
TI  - On the Darboux integrability of the Painlevé II equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 60
EP  - 75
VL  - 22
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.996441
DO  - 10.1080/14029251.2015.996441
ID  - Llibre2021
ER  -