Limits of the uni-directional pulse propagation approximation

TL;DR

This paper investigates the limitations of the uni-directional pulse propagation approximation by comparing it with bi-directional models, using the method of characteristics and numerical simulations to analyze shock formation and wave coupling.

Contribution

It provides a quantitative analysis of the shock distance differences between uni- and bi-directional models, highlighting the effects of the approximation in nonlinear dispersionless media.

Findings

Uni-directional approximation overestimates shock distance.

Numerical results support the theoretical predictions.

Coupling between forward and backward waves is significant in nonlinear media.

Abstract

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.