Wave breaking in the short-pulse equation

Sufficient conditions for wave breaking are found for the short-pulse 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.

💡 Research Summary

The paper investigates finite‑time wave breaking (gradient blow‑up) for the short‑pulse equation (SPE), a model that describes ultra‑short optical pulses whose duration is only a few carrier cycles. The SPE in its standard form,
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