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Evolution Equations and Reduction Approaches for Nonlinear Waves in Solids

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

Abstract

We outline some theoretical procedures which permit to get an insight into the nonlinear structure of mathematical models of interest in wave propagation. First, by assuming the original governing system of first order PDE’s to take into account dissipative effects of different order of magnitude, we derive for the wave amplitude the evolution equation which, in same cases, involves a hierarchy of nonlinear wave opera­tors. Later we focus our attention on developing reduction techniques in order to find out exact solutions to quasilinear nonhomogeneous systems of first order involving two dependent and two independent variables.

Keywords

Wave Propagation Nonlinear Wave Reduction Approach Governing Model Characteristic Speed 
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Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • D. Fusco
    • 1
  1. 1.Dipartimento di MatematicaUniversità di MessinaSant’Agata, MessinaItaly

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