Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis

Details Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis

2003-12-19

arxiv.org/abs/math-ph/0312048v1

Physics

Mathematical Physics

8 pages, to appear in the proceedings of the Fifth International Conference "Symmetry in Nonlinear Mathematical Physics" (Kiev

Scientific paper

The generalized Henon-Heiles system has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as Laurent series, depending on three parameters. The obtained series converge in some ring. One of parameters determines the singularity point location, other parameters determine coefficients of series. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions. The Painleve test can be used not only to construct local solutions as the Laurent series but also to find elliptic solutions.

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