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We present a system of modulation equations that approximate the focusing of the nonlinear Schr\"odinger equation in the presence of a small normal time dispersion (TDNLS). Since the modulation equations are much easier for analysis and for numerical simulations, they can be used to get a general picture of the TDNLS focusing. Analytical and numerical agreement between the modulation equations and the TDNLS is established.
Fibich et al. (Wed,) studied this question.