"Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media" by Darryl H. Yong and Randall J. Leveque
 

Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media

Document Type

Book Chapter

Department

Mathematics (HMC)

Publication Date

2003

Abstract

The one-dimensional elastic wave equations for compressional waves have the form (1)

\hfill∈t(x,t)−ux(x,t)=0\hfill(ρ(x)u(x,t))t−σ(∈(x,t),x)x=0

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.

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© 2003 Springer

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