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Nonlinear hyperbolic wave propagation in a one-dimensional random medium

โœ Scribed by John B. Thoo; John K. Hunter

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
243 KB
Volume
37
Category
Article
ISSN
0165-2125

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โœฆ Synopsis

We use an asymptotic expansion introduced by Benilov and Pelinovski ศ‹ to study the propagation of a weakly nonlinear hyperbolic wave pulse through a stationary random medium in one space dimension. We also study the scattering of such a wave by a background scattering wave. The leading-order solution is non-random with respect to a realization-dependent reference frame, as in the linear theory of O'Doherty and Anstey. The wave profile satisfies an inviscid Burgers equation with a nonlocal, lower-order dissipative and dispersive term that describes the effects of double scattering of waves on the pulse. We apply the asymptotic expansion to gas dynamics, nonlinear elasticity, and magnetohydrodynamics.

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