Construction of global multi-valued solutions for dynamic systems

The algebraic method for the search of the analytic form of solutions for autonomous nonintegrable systems is proposed. This algorithm is a generalization of the known methods for the search of singlevalued solutions. We seek solutions as polynomials in a function, which satisfies some autonomous polynomial first order differential equation. To find analytic solutions we use local (the Puiseux series) solutions of the initial nonintegrable system. The local solutions can be obtained by the Painleve analysis. Given algorithm can be automatized due to computer algebra systems.
Keywords: nonintegrable systems, the Painleve analysis, a polynomial potential, the Puiseux series, multi-valued functions, special solutions.

Document number: 2004--18/757

Authors: Vernov S.Yu.


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