2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165504I 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.6 pages, 6 figures; this version contains an additional appendix not present in the published versionOpticstext