A Semilinear Wave Sector in Force-Free Electrodynamics

TL;DR

This paper presents a reduction of force-free electrodynamics to a semilinear wave equation, enabling explicit solutions and analysis of complex configurations in Minkowski spacetime.

Contribution

It introduces an ansatz that simplifies the nonlinear system to a semilinear wave equation, providing new explicit solutions and insights into force-free fields.

Findings

Derived explicit time-dependent solutions including type-changing configurations.

Identified null kink-type solutions with finite energy per unit transverse area.

Analyzed the kernel distribution for traveling-wave solutions in the magnetically dominated regime.

Abstract

We introduce an ansatz for force-free electrodynamics in Minkowski spacetime under which the nonlinear system reduces to a semilinear scalar wave equation depending on two spacetime variables. This reduction yields explicit time-dependent solutions, including type-changing configurations with finite energy per unit transverse area and a null kink-type example. For traveling-wave solutions in the magnetically dominated regime, the kernel distribution of the field defines minimal field-sheet foliations.