Open Access
VOL. 6 | 2005 Single-Valued and Multivalued Solutions for the Generalized Hénon-Heiles System with an Additional Nonpolynomial Term
Sergey Yu Vernov

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2005: 297-309 (2005) DOI: 10.7546/giq-6-2005-297-309


The generalized Hénon–Heiles system with an additional non-polynomial term is considered. The standard method for the search of the elliptic solutions is a transformation of an initial nonlinear polynomial differential equation into a nonlinear algebraic system. It has been demonstrated that the use of the Laurent-series solutions allows to simplify the resulting algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial equation in the form of the Laurent or Puiseux series we use algorithm of the Painlevé test.


Published: 1 January 2005
First available in Project Euclid: 12 June 2015

zbMATH: 1112.37044
MathSciNet: MR2161776

Digital Object Identifier: 10.7546/giq-6-2005-297-309

Rights: Copyright © 2005 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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