Nonlinear waves in a dispersive vacuum described with a high order derivative electromagnetic Lagrangian

TL;DR

This paper develops a Lorentz-invariant electromagnetic Lagrangian with higher derivatives to model dispersive effects in the quantum vacuum, deriving exact nonlinear wave solutions including solitons and periodic waves.

Contribution

It introduces a novel high-order derivative Lagrangian for electromagnetic fields that captures dispersive effects in the quantum vacuum, extending previous models.

Findings

Derived exact solutions of nonlinear wave equations in the dispersive vacuum

Recovered Korteveg-de Vries type periodic waves and solitons

Discussed conceptual limitations of the higher derivative approach

Abstract

In this article we use an electromagnetic Lagrangian constructed so as to include dispersive effects in the description of an electromagnetic wave propagating in the Quantum Electrodynamic Vacuum. This Lagrangian is Lorentz invariant, includes contributions up to six powers in the electromagnetic fields and involves both fields and their first derivatives. Conceptual limitations inherent to the use of this higher derivative Lagrangian approach are discussed. We consider the one-dimensional spatial limit and obtain an exact solution of the nonlinear wave equation recovering the Korteveg-de Vries type periodic waves and solitons given in S. V. Bulanov et al., Phys. Rev. D, 101, 016016 (2020).