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Normal Modes and Localization in Nonlinear Systems

Normal Modes and Localization in Nonlinear Systems

Alexander F. Vakakis, Leonid I. Manevitch, Yuri V. Mikhlin, Valery N. Pilipchuk, Alexandr A. Zevin

ISBN: 978-3-527-61786-9

Jan 2008

552 pages

Select type: O-Book

Description

This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.
NNMs in Discrete Oscillators: Qualitative Results.

NNMs in Discrete Oscillators: Quantitative Results.

Stability and Bifurcations of NNMs.

Resonances of Discrete Systems Close to NNMs.

The Method of Nonsmooth Temporal Transformations (NSTTs).

Nonlinear Localization in Discrete Systems.

NNMs in Continuous Systems.

Nonlinear Localization in Systems of Coupled Beams.

Nonlinear Localization in Other Continuous Systems.

References.

Index.