Physical Sciences and Mathematics Commons^™

Solitary Waves In Layered Nonlinear Media, Randall J. Leveque, Darryl H. Yong

All HMC Faculty Publications and Research

We study longitudinal elastic strain waves in a one-dimensional periodically layered medium, alternating between two materials with different densities and stress-strain relations. If the impedances are different, dispersive effects are seen due to reflection at the interfaces. When the stress-strain relations are nonlinear, the combination of dispersion and nonlinearity leads to the appearance of solitary waves that interact like solitons. We study the scaling properties of these solitary waves and derive a homogenized system of equations that includes dispersive terms. We show that pseudospectral solutions to these equations agree well with direct solutions of the hyperbolic conservation laws in the …