Geodesic
General Solution for Hamiltonians with Extended Cubic and Quartic Potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 148-159

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In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases $1:6:1$ and $1:6:8$.
Mots-clés : Hénon–Heiles, soliton equations.
Keywords: Hamiltonian systems, separation of variables, nonlinear equations, hyperelliptic functions 
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     author = {C. Verhoeven and M. Musette and R. Conte},
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C. Verhoeven; M. Musette; R. Conte. General Solution for Hamiltonians with Extended Cubic and Quartic Potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 148-159. http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a12/