Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media

Randall J. LeVeque () and Darryl H. Yong ()
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Randall J. LeVeque: University of Washington, Department of Applied Mathematics
Darryl H. Yong: California Institute of Technology, Department of Applied and Computational Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 43-51 from Springer

Abstract: Abstract The one-dimensional elastic wave equations for compressional waves have the form (1) $$ \begin{array}{*{20}{c}} \hfill {{{ \in }_{t}}(x,t) - {{u}_{x}}(x,t) = 0} \\ \hfill {{{{(\rho (x)u(x,t))}}_{t}} - \sigma {{{( \in (x,t),x)}}_{x}} = 0} \\ \end{array} $$ where ε(x, t) is the strain and u(x, t) the velocity. We consider a heterogeneous material with the density specified by ρ(x) and a nonlinear constitutive relation for the stress given by a function σ(∈, x) that also varies explicitly with x. This is a hyperbolic system of conservation laws with a spatially-varying flux function, q t + f(q, x) x = 0.

Keywords: Solitary Wave; Finite Volume Method; Hyperbolic System; Wave Train; Integral Curve (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_3

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DOI: 10.1007/978-3-642-55711-8_3

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