Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media

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Book Chapter


Mathematics (HMC)

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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.

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