Abstract
A detailed description is given of integrable cases of the generalized Henon–Heiles systems which differs from the standard H–H ones by the term α/q22. Their connection with fifth-order one-component soliton equations is discussed. Lax representations are constructed, and the bi-Hamiltonian formulation of dynamics is given. It is also shown that the gH–H system can be mapped onto another system of Newton equations with a nonstandard Hamiltonian structure.
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