Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.2, pp.121-132

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.2, pp.121-132

Canonical Perturbation Theory and Lie Transforms: Application to Nonlinear Resonant Wave-Particle Interaction.
Y. Kominis

Resonant wave-particle interactions has been one of the main paradigms, on which the modern theory of complex dynamics and chaos has been applied. In this work, these interactions are studied in the context of the Hamiltonian formalism and the Canonical Perturbation Theory (CPT) with utilization of Lie Transform techniques (LT). The canonical perturbation method for single particle motion is reviewed and extended in order to provide results for the collective particle behavior under interaction with wave fields of either localized or periodic profiles. Analytical expressions for the calculation of phase-averaged quantities of physical interest as well as diffusion equations are derived.
Key words: perturbation theory, resonant wave-particle interactions, Lie transform techniques

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