Modulational Instability in Equations of KdV Type
Abstract
It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.
Keywords
Cite
@article{arxiv.1501.02788,
title = {Modulational Instability in Equations of KdV Type},
author = {Jared C. Bronski and Vera Mikyoung Hur and Mathew A. Johnson},
journal= {arXiv preprint arXiv:1501.02788},
year = {2015}
}
Comments
40 pages. To appear in upcoming title in Lecture Notes in Physics