2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120302The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schrödinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques.9 pages, 3 figures, to appear in Phys. Rev. EPattern Formation and Solitonstext