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.
© 2007 Optical Society of America
Original Manuscript: April 13, 2007
Revised Manuscript: July 6, 2007
Manuscript Accepted: July 9, 2007
Published: August 23, 2007
P. Kinsler, "Limits of the unidirectional pulse propagation approximation," J. Opt. Soc. Am. B 24, 2363-2368 (2007)