# Properties of Finite Amplitude Electromagnetic Waves propagating in the Quantum Vacuum

## TL;DR

This paper investigates the nonlinear behavior of counter-propagating electromagnetic waves in the quantum vacuum using Heisenberg-Euler formalism, revealing phenomena like wave steepening, harmonic generation, shock formation, and pair creation.

## Contribution

It provides exact solutions for nonlinear electromagnetic wave equations in quantum vacuum and explores their complex propagation properties and phenomena.

## Key findings

- Wave steepening and harmonic generation observed.
- Electromagnetic shock waves can form in quantum vacuum.
- Electron-positron pairs are generated at shock fronts.

## Abstract

We study two counter-propagating electromagnetic waves in the vacuum within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. We show that the non-linear field equations decouple for ordinary wave case and can be solved exactly. We solve the non-linear field equations assuming the solution in a form of a Riemann wave. We discuss the properties of the nonlinear electromagnetic wave propagating in the quantum vacuum, such as the wave steepening, subsequent generation of high order harmonics and electromagnetic shock wave formation with electron-positron pair generation at the shock wave front.