Limits of the unidirectional pulse propagation approximation

I apply the method of characteristics to both bidirectional and unidirectional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the unidirectional 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.

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