This article is cited in 18 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

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.

DOI: 10.4213/tmf205

 English version: Theoretical and Mathematical Physics, 2003, 135:3, 792–801

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