Solitary Waves in Layered Nonlinear Media

Authors

Randall J. Leveque, University of Washington - Seattle Campus
Darryl H. Yong, Harvey Mudd CollegeFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

6-12-2003

Abstract

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 layered medium using a high-resolution finite volume method. For particular parameters we also show how the layered medium can be related to the Toda lattice, which has discrete soliton solutions.

Comments

First published by SIAM Journal of Applied Mathematics, vol. 63, no. 5 (June 2003), by the Society for Industrial and Applied Mathematics.

Rights Information

© 2003 Society for Industrial and Applied Mathematics

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1137/S0036139902408151

Recommended Citation

Leveque, RJ, Yong, DH. Solitary waves in layered nonlinear media. J App Math. 2003;63(5): 1539-1560.