Geodesic
Constructing Solutions for the Generalized H\'enon--Heiles System Through the Painlev\'e Test
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 409-419

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The generalized Hénon–Heiles system is considered. New special solutions for two nonintegrable cases are obtained using the Painlevé test. The solutions have the form of the Laurent series depending on three parameters. One parameter determines the singularity-point location, and the other two parameters determine the coefficients in the Laurent series. For certain values of these two parameters, the series becomes the Laurent series for the known exact solutions. It is established that such solutions do not exist in other nonintegrable cases.
Keywords: nonintegrable systems, Painlevé test, singularity analysis, polynomial potential, Hénon–Heiles system, elliptic functions.
Mots-clés : Laurent series 
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     author = {S. Yu. Vernov},
     title = {Constructing {Solutions} for the {Generalized} {H\'enon--Heiles} {System} {Through} the {Painlev\'e} {Test}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {409--419},
     publisher = {mathdoc},
     volume = {135},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a3/}
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S. Yu. Vernov. Constructing Solutions for the Generalized H\'enon--Heiles System Through the Painlev\'e Test. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 409-419. http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a3/