Canonical separating coordinates in the generalized cubic H'enon-Heiles systems
The study investigates three integrable cubic Hénon–Heiles systems (Kaup–Kupershmidt, KdV5, and Sawada–Kotera) using bi-Hamiltonian geometry. The method involves constructing compatible Poisson deformations to find control matrices whose eigenvalues yield canonical separating coordinates. The primary achievement is the explicit construction of conjugate momenta for the Kaup–Kupershmidt case in a fixed coordinate system.