Symmetric solutions to the four dimensional degenerate Painlevé type equation NY^A₄

Abstract

We have classified symmetric solutions around the origin to the four dimensional degenerate Painlevé type equation NY^A₄ with generic values of parameters. We obtained sixteen meromorphic solutions, which are transformed each other by the Bäcklund transformation. We calculated the linear monodromy for one of them, explicitly.

Keywords:

• the four dimensional degenerate Painlevé type equation
• monodromy data
• Bäcklund transformation

2000 Mathematics Subject Classification:

• Primary 34M55
• Secondary 33C15