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DY: Dynamik und Statistische Physik
DY 34: Poster
DY 34.34: Poster
Monday, March 7, 2005, 15:30–18:00, Poster TU D
High-Order Variational Calculation for Periodic Orbits — •Axel Pelster1, Alexey Novikov2, Ulrich Kleinkathöfer2, and Michael Schreiber2 — 1Fachbereich Physik, Universität Duisburg-Essen, Essen, Germany — 2Institut für Physik, Technische Universität Chemnitz, Chemnitz, Germany
Following Ref. [1], we develop a convergent variational perturbation theory for periodic orbits of nonlinear dynamical systems. An optimization with respect to artifically introduced variational parameters allows to convert divergent weak-coupling series for periodic orbits into convergent strong-coupling series. At first, the power of the theory is illustrated by applying it to the undamped Duffing oscillator where we obtain an exponentially fast convergence for the time-periodic solution. Then we investigate how our theory can be extended to the damped Duffing oscillator as this model system has many technical similarities with the quantum mechanical damped harmonic oscillator [2].
[1] A. Pelster, H. Kleinert, and M. Schanz: Phys. Rev. E 67, 016604 (2003).
[2] A. Novikov, U. Kleinekathöfer, and M. Schreiber: J. Phys. A 37, 3019 (2004).