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.
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Maugin, G.A. (1994). Physical and Mathematical Models of Nonlinear Waves in Solids. In: Jeffrey, A., Engelbrecht, J. (eds) Nonlinear Waves in Solids. CISM Courses and Lectures, vol 341. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2444-4_3
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