Wave breaking in the short-pulse equation

Abstract

Sufficient conditions for wave breaking are found for the shortpulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the short-pulse equation and holds both on an infinite line and in a periodic domain. Numerical illustrations of the finite-time wave breaking are given in a periodic domain. Contents 1. Introduction 291 2. Wave breaking on an infinite line 294 3. Wave breaking in a periodic domain 303 4. Numerical evidence of wave breaking 305 References 309