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arXiv · 0704.3057

Explosive instability due to 4-wave mixing

Benjamin R. Safdi·Harvey Segur
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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.

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Benjamin R. Safdi, Harvey Segur. 2007-04-23. Explosive instability due to 4-wave mixing. https://doi.org/10.1103/physrevlett.99.245004

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