Higher-order corrections to the short-pulse equation

TL;DR

This paper derives an extended short-pulse equation using renormalization group methods to better model higher-order effects in pulse propagation within nonlinear media, validated through numerical simulations.

Contribution

It introduces a novel higher-order correction to the short-pulse equation and demonstrates its effectiveness in capturing complex pulse dynamics.

Findings

The extended equation accurately models higher-order effects.

Numerical simulations show improved pulse propagation predictions.

One- and two-soliton solutions validate the new model.

Abstract

Using renormalization group techniques, we derive an extended short- pulse equation as approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higher- order effects on pulse propagation in cubic nonlinear media. We illustrate our findings using one- and two-soliton solutions of the first-order short-pulse equation as initial conditions in the nonlinear wave equation.