Geodesic
General Solution for Hamiltonians with Extended Cubic and Quartic Potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 148-159 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 
@article{TMF_2003_134_1_a12,
     author = {C. Verhoeven and M. Musette and R. Conte},
     title = {General {Solution} for {Hamiltonians} with {Extended} {Cubic} and {Quartic} {Potentials}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {148--159},
     year = {2003},
     volume = {134},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a12/}
}
TY  - JOUR
AU  - C. Verhoeven
AU  - M. Musette
AU  - R. Conte
TI  - General Solution for Hamiltonians with Extended Cubic and Quartic Potentials
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 148
EP  - 159
VL  - 134
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a12/
LA  - ru
ID  - TMF_2003_134_1_a12
ER  - 
%0 Journal Article
%A C. Verhoeven
%A M. Musette
%A R. Conte
%T General Solution for Hamiltonians with Extended Cubic and Quartic Potentials
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 148-159
%V 134
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a12/
%G ru
%F TMF_2003_134_1_a12
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/

[1] T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A, 25 (1982), 1257–1264 | DOI | MR

[2] Y. F. Chang, M. Tabor, J. Weiss, J. Math. Phys., 23 (1982), 531–538 | DOI | MR | Zbl

[3] B. Grammaticos, B. Dorizzi, R. Padjen, Phys. Lett. A, 89 (1982), 111–113 | DOI | MR

[4] A. P. Fordy, Physica D, 52 (1991), 204–210 | DOI | MR | Zbl

[5] S. Baker, Squared eigenfunction representation of integrable hierarchies, Ph. D. Thesis, University of Leeds, Leeds, 1995 | Zbl

[6] C. Verhoeven, M. Musette, R. Conte, J. Math. Phys., 43 (2002), 1906–1915 ; E-print nlin.SI/0112030 | DOI | MR | Zbl

[7] B. Grammaticos, B. Dorizzi, A. Ramani, J. Math. Phys., 24 (1983), 2289–2295 | DOI | MR | Zbl

[8] J. Hietarinta, J. Math. Phys., 25 (1984), 1833–1844 | DOI | MR

[9] J. Hietarinta, Phys. Rep., 147 (1987), 87–154 | DOI | MR

[10] B. Grammaticos, B. Dorizzi, A. Ramani, J. Math. Phys., 25 (1984), 3470–3473 | DOI | MR

[11] V. Ravoson, A. Ramani, B. Grammaticos, Phys. Lett. A, 191 (1994), 91–95 | DOI | MR | Zbl

[12] F. J. Romeiras, J. Math. Phys., 36 (1995), 3559–3565 | DOI | MR | Zbl

[13] S. V. Manakov, ZhETF, 65 (1973), 505–516

[14] R. Garnier, Rendiconti del Circolo Matematico di Palermo, 43 (1919), 3559–3565 | DOI

[15] S. Wojciechowski, Physica Scripta, 31 (1985), 433–438 | DOI | MR | Zbl

[16] V. G. Drinfeld, V. V. Sokolov, Tr. semin. L. S. Soboleva, 2 (1981), 5–9 | MR | Zbl

[17] S. Baker, V. Z. Enolskii, A. P. Fordy, Phys. Lett. A, 201 (1995), 167–174 | DOI | MR | Zbl

[18] J. Satsuma, R. Hirota, J. Phys. Soc. Japan, 51 (1982), 3390–3397 | DOI | MR

[19] A. P. Fordy, J. Gibbons, J. Math. Phys., 21 (1980), 2508–2510 | DOI | MR | Zbl

[20] M. Błaszak, S. Rauch-Wojciechowski, J. Math. Phys., 35 (1994), 1693–1709 | DOI | MR

[21] V. Ravoson, L. Gavrilov, R. Caboz, J. Math. Phys., 34 (1993), 2385–2393 | DOI | MR | Zbl

[22] F. J. Romeiras, J. Phys. A, 28 (1995), 5633–5642 | DOI | MR | Zbl