Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test

S. Yu. Vernov

Submitted on 27 July 2004


The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the elliptic solutions we transform an initial nonlinear differential equation in a nonlinear algebraic system in parameters of the Laurent-series solutions of the initial equation. The number of unknowns in the obtained nonlinear system does not depend on number of arbitrary coefficients of the used first order equation. In this paper we describe the corresponding algorithm, which has been realized in REDUCE and Maple.


Comment: The proceedings of the International Conference "Computer Algebra in Scientific Computing" (CASC 2004, Jule 12 - 19, 2004, St. Petersburg, Russia), eds. V.G. Ganzha, E.W. Mayr, E.V. Vorozhtsov, Technische Universitat, Munchen, Garching, Germany, 2004, pp. 457-465

Subjects: Nonlinear Sciences - Exactly Solvable and Integrable Systems; Astrophysics - Solar and Stellar Astrophysics; Computer Science - Mathematical Software; Mathematical Physics; Mathematics - Dynamical Systems