# 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.

## Rights Information

© 2003 Springer

## Terms of Use & License Information

## DOI

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

## Recommended Citation

Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25–29 2002. Hou, Thomas Y.; Tadmor, Eitan (Eds.) 2003, XXVIII, 961 p. ISBN 978-3-540-44333-9 pp 43-51 “Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media” by Randall J. LeVeque, Darryl H. Yong