Diffractons: solitary waves created by diffraction in periodic media
Pattern Formation and Solitons
2013-12-17 v1
Abstract
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically-varying sound speed. They share some properties with known classes of solitary waves, but possess important differences as well.
Cite
@article{arxiv.1312.4122,
title = {Diffractons: solitary waves created by diffraction in periodic media},
author = {David I. Ketcheson and Manuel Quezada de Luna},
journal= {arXiv preprint arXiv:1312.4122},
year = {2013}
}