Explosive instability due to 4-wave mixing
Exactly Solvable and Integrable Systems
2009-11-13 v1
Abstract
It is known that an explosive instability can occur when nonlinear waves propagate in certain media that admit 3-wave mixing. The purpose of this paper is to show that explosive instabilities can occur even in media that admit no 3-wave mixing. Instead, the instability is caused by 4-wave mixing: four resonantly interacting wavetrains gain energy from a background, and all blow up in a finite time. Unlike singularities associated with self-focussing, these singularities can occur with no spatial structure - the waves blow up everywhere in space, simultaneously.
Keywords
Cite
@article{arxiv.0704.3057,
title = {Explosive instability due to 4-wave mixing},
author = {Benjamin R. Safdi and Harvey Segur},
journal= {arXiv preprint arXiv:0704.3057},
year = {2009}
}