We find and study a two-parameter family of coupled Painlevé II systems in dimension four, which can be obtained by a degeneration from the systems of type $A_4^{(1)}$. These systems are compared with other types of coupled Painlevé II systems from the viewpoint of the local index. We also give the phase spaces for these systems.
Publié le : 2006-12-14
Classification:
Accessible singularity,
local index,
Painlevé equations,
34M55,
34M45
@article{1170347688,
author = {Sasano, Yusuke},
title = {Coupled Painlev\'e II systems in dimension four and the systems of type $A\_4^{(1)}$},
journal = {Tohoku Math. J. (2)},
volume = {58},
number = {1},
year = {2006},
pages = { 529-548},
language = {en},
url = {http://dml.mathdoc.fr/item/1170347688}
}
Sasano, Yusuke. Coupled Painlevé II systems in dimension four and the systems of type $A_4^{(1)}$. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp. 529-548. http://gdmltest.u-ga.fr/item/1170347688/