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Hierarchical methods, hierarchy & hierarchical asymptotic methods in electrodynamics, vol. 1 (fundamental theories of physics/123), Softcover reprint of the original 1st ed. 2004 Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics, Volume 1 Coll. Fundamental Theories of Physics, Vol. 123

Langue : Français

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Couverture de l’ouvrage Hierarchical methods, hierarchy & hierarchical asymptotic methods in electrodynamics, vol. 1 (fundamental theories of physics/123)
This monograph consists of two volumes and provides a unified comprehensive presentation of a new hierarchic paradigm and discussions of various applications of hierarchical methods for nonlinear electrodynamic problems. Volume 1 is the first book, in which a new hierarchical model for dynamic non-linear systems is described and analysed and a set of new hierarchical principles is discussed. The modern hierarchic asymptotic methods are set forth systematically, taking into account specific features of electrodynamic problems, and the phenomenon of hierarchy in electrodynamics, in itself, is thoroughly discussed from a new point of view. A set of hierarchical asymptotic calculative methods of two types is discussed in detail. The methods of the first type are destined for asymptotic integration of non-linear differential equations with total derivatives and with multifrequency (including multi-scale) non-linear right hand parts. These are the Van der Pol method, Krylov-Bogolyubov method, Bogolyubov-Zubarev method and their hierarchical versions. The methods of the second type include the method of slowly varying amplitudes, the method of averaged characteristics, the methods of averaged kinetic and quasihydrodynamic equations, and some other. These methods are intended for asymptotic integration of non-linear differential equations with partial derivatives and multifrequency (including multi-scale) right hand parts. Detailed calculative technologies for practical application of all mentioned methods are illustrated by examples of real electrodynamic systems (free electron lasers, undulative induction accelerators, systems for transformation of laser signals, etc.).
Acknowledgments. Preface. 1. General Ideas, Concepts, Definitions, and other Preliminary Information. 2. Hierarchy and Hierarchical Systems. 3. Hierarchical Asymptotic Methods. General Ideas. 4. Hierarchical Systems with fast Rotating Phases. 5. Hierarchical Systems with Fast Rotating Phases. Examples of Practical Applications. 6. Hierarchical Systems with Partial Derivatives. Method of Averaged Characteristics. 7. Example: Application of the Method of Averaged Characteristics in Nonlinear Theory of the Two-stream Instability. 8. Hierarchical Systems with Partial Derivatives. Some Other Asymptotic Methods. Appendices. Index.

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