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Geometric Optics for Surface Waves in Nonlinear Elasticity (Memoirs of the American Mathematical Society)

Light, Optics & Laser

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About the Author Jean-Francois Coulombel, Universite de Nantes, FranceMark Williams, University of North Carolina, Chapel Hill, NC Product Description This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as ``the amplitude equation'', is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions $u^{\varepsilon} $ to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength $\varepsilon $, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to $u^{\varepsilon}$ on a time interval independent of $\varepsilon $. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.

Product Specifications

Format: paperback
ASIN: 1470440377
Category: Books > Subjects > Science, Nature & Maths > Physics > Light, Optics & Laser
Domain: Amazon UK
Release Date: 30 January 2020
Listed Since: 18 December 2019

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Geometric Optics for Surface Waves in Nonlinear Elasticity (Memoirs of the American Mathematical Society)

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