Higher-order corrections to the short-pulse equation

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.

References in corpus (2)

• The short pulse equation is integrable
• On integrability of the vector short pulse equation

Cited by in corpus (1)

• Propagation of ultra-short solitons in stochastic Maxwell's equations