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Nonlinear Duality Between Elastic Waves and Quasi-particles

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Selected Topics in Nonlinear Wave Mechanics

Abstract

Some systems governed by a set of partial differential equations present the necessary ingredients (nonlinearity and dispersion) in appropriate doses so as to become the arena of the propagation and interactions of solitary waves. In general such systems are not exactly integrable in the sense of soliton theory. But some of their nearly solitonic solutions can nonetheless be apprehended as quasi-particles in a certain dynamics that depends on the original system. The present chapter considers this reductive representation of nonlinear dynamical solutions for physical systems issued from solid mechanics, and more particularly elasticity with a microstructure of various origin. A whole collection of “point-mechanics” emerges thus, among which the simpler ones are Newton's and Lorentz-Einstein’s. This quasi-particle representation is intimately related to the existence of conservation laws for the system under study and the recent recognition of the essential role played by fully material balance laws in the continuum mechanics of inhomo-geneous and defective elastic bodies.

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Authors and Affiliations

  1. Laboratoire de Modélisation en Mécanique, Université Pierre-et-Marie Curie, Tour 6, 4 place Jussieu, Case 162, F-75252, Paris Cedex 05, France

    G. A. Maugin

  2. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA

    C. I. Christov

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  1. G. A. Maugin
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Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA

    C. I. Christov

  2. Institute of Structronics, 275 Slater Street, Ottawa, K1P-5H9, Canada

    A. Guran

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Maugin, G.A., Christov, C.I. (2002). Nonlinear Duality Between Elastic Waves and Quasi-particles. In: Christov, C.I., Guran, A. (eds) Selected Topics in Nonlinear Wave Mechanics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0095-6_4

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  • DOI: https://doi.org/10.1007/978-1-4612-0095-6_4

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