Tohoku Mathematical Journal
2006

December
SECOND SERIES VOL. 58, NO. 4

Tohoku Math. J.
58 (2006), 529-548

Title COUPLED PAINLEVÌ II SYSTEMS IN DIMENSION FOUR AND THE SYSTEMS OF TYPE $A_4^{(1)}$

Author Yusuke Sasano

(Received April 12, 2005, revised August 2, 2006)
Abstract. We find and study a two-parameter family of coupled Painleve 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.

2000 Mathematics Subject Classification. Primary 34M55; Secondary 34M45.

Key words and phrases. Accessible singularity, local index, Painlevé equations.

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