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REVIEW ARTICLES: General Lectures

Qualitative Aspects of Nonlinear Wave Motion: Complexity and Simplicity

[+] Author and Article Information
J. Engelbrecht

Institute of Cybernetics, Estonian Academy of Sciences, EE0026 Tallinn, Estonia

Appl. Mech. Rev 46(12), 509-518 (Dec 01, 1993) (10 pages) doi:10.1115/1.3120312 History: Online April 29, 2009

Abstract

The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed.

Copyright © 1993 by American Society of Mechanical Engineers
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