Limits of the uni-directional pulse propagation approximation P. Kinsler, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom. J. Opt. Soc. Am. B24, 2363 (2007). arXiv:0707.0986 I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the uni-directional approximation used in many pulse propagation models. Results from numerical simulations support the theoretical predictions, and reveal the nature of the coupling between forward and backward waves.