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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 135, Number 3, Pages 409–419
DOI: https://doi.org/10.4213/tmf205 (Mi tmf205) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Constructing Solutions for the Generalized Hénon–Heiles System Through the Painlevé Test

S. Yu. Vernov

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
Full-text PDF (233 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf205
Abstract: 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, Laurent series, elliptic functions.
English version:
Theoretical and Mathematical Physics, 2003, Volume 135, Issue 3, Pages 792–801
DOI: https://doi.org/10.1023/A:1024074702960
Bibliographic databases:
Language: Russian
Citation: S. Yu. Vernov, “Constructing Solutions for the Generalized Hénon–Heiles System Through the Painlevé Test”, TMF, 135:3 (2003), 409–419; Theoret. and Math. Phys., 135:3 (2003), 792–801
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v135/i3/p409
    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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