Nonlinear Wave Motion and Evolution Equations

  • J. Engelbrecht
Part of the CISM Courses and Lectures book series (CISM, volume 341)


In Section 1 the basic wave theory is briefly discussed with attention paid to the various types of waves and their velocities. Section 2 reviews the sources of nonlinearities from the viewpoint of mathematical models and gives some answers to the question about the use of nonlinearities. Section 3 concerns the derivation of mathematical models on the basis of the continuum mechanics. In Section 4, the derivation of evolution equations is discussed, analyzing asymptotic (reductive perturbation), iterative and spectral methods as well as the method of approximate (etalon) evolution equations. The emphasis is put on the correspondence of mathematical procedures to physical phenomena. Section 5 starts with the analysis of levels of nonlinearities and later gives some examples of case studies. Complexity and simplicity of nonlinear wave motion are briefly discussed.


Evolution Equation Solitary Wave Helmholtz Free Energy Wave Profile Quadratic Nonlinearity 
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Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • J. Engelbrecht
    • 1
  1. 1.Estonian Academy of SciencesTallinnEstonia

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