title: Explosive Instability due to four-wave mixing.
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 Letter 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 wave trains gain energy from a background, and all blowup in a finite time. Unlike singularities associated with self-focussing, these singularities can occur with no spatial structure-the waves blowup everywhere in space simultaneously. We have not yet investigated the effect of spatial structure on a 4-wave explosive instability.
authors.affiliation: Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
authors.forename: Benjamin R
authors.initials: BR
authors.lastname: Safdi
authors.forename: Harvey
authors.initials: H
authors.lastname: Segur