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Physical and Mathematical Models of Nonlinear Waves in Solids

  • G. A. Maugin
Part of the CISM Courses and Lectures book series (CISM, volume 341)

Abstract

In a first part (Sections 1 to 4), continuum and discrete (lattice) models of solids such as in elasticity and anelasticity are introduced with special attention paid to nonlinearity and dispersion. This is extended to solids with a microstructure of mechanical or electromagnetic origin. The second part (Sections 5 to 7) exemplifies models and properties of nonlinear-wave problems with an emphasis on solitary waves and soli-tons. Both exactly integrable and nearly integrable systems are considered. Systems governed by sine-Gordon, Boussinesq, Korteweg-de Vries, nonlinear Schrödinger and Zakharov equations or systems belong to the first class. Generalized Boussinesq, Zakharov and sine-Gordon-d’Alembert systems belong to the second class. The main properties of such systems are illustrated by computer-generated figures. Energy and pseudomomentum balances are presented as useful tools in such studies. Solitonic and dissipative structures are discriminated.

Keywords

Solitary Wave Nonlinear Wave Boussinesq Equation Envelope Soliton Wave Momentum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • G. A. Maugin
    • 1
  1. 1.Pierre et Marie Curie UniversityParisFrance

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