Abstract
The nonlinear Schr\odinger equation (NSE) provides a powerful tool for the analysis of ultrafast nonlinear-optical dynamics, including a vast class of optical solitons. Here, we show, however, that the photon-number integral of the NSE differs from the physical number of photons, conserved by more general field evolution equations. This difficulty is traced to the optical shock term, which is dropped in the NSE, making nonlinear coupling in NSE-based models frequency independent and leading to unphysical predictions for ultrabroadband, octave-spanning field waveforms.
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