An application of the Kowalewski Conditions

© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature. There are three cubic Hénon-Heiles systems which are integrable in the Liouville sense. In this paper we focus our attention on one of them, the so called Kaup-Kupershmidt (KK) system. Under the restricting condition c= 0 , the equations of movement of this system can be separated and integrated using coordinates originally discovered by Ravoson, Gabrilov and Caboz. In this paper we show that the adoption of a different point of view provides a natural generalization of these coordinates and separate the generic cas