Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media
The one-dimensional elastic wave equations for compressional waves have the form (1)
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.
© 2003 Springer
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