Construction of Solutions for Nonintegrable Systems with the Help of the Painleve Test

摘要

The generalized Henon-Heiles system with an additional nonpolynomial term has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as converging Laurent series, depending on three parameters. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known elliptic solutions. The calculations have been made with use of computer algebra system REDUCE. The obtained local solutions can assist to find the elliptic three parameters solutions. The corresponding algorithm has been realized in REDUCE and Maple.