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Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • Randall J. LeVeque

    (University of Washington, Department of Applied Mathematics)

  • Darryl H. Yong

    (California Institute of Technology, Department of Applied and Computational Mathematics)

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.

Suggested Citation

  • Randall J. LeVeque & Darryl H. Yong, 2003. "Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 43-51, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_3
    DOI: 10.1007/978-3-642-55711-8_3
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