Numerical Simulation of Electromagnetic Solitons and their Interaction with Matter

TL;DR

This paper explores the existence and behavior of electromagnetic solitons in vacuum through corrected Maxwell models, employing finite-difference simulations to analyze their interactions with matter and classical dispersion phenomena.

Contribution

It introduces a modified Maxwell model that admits solitons in vacuum and demonstrates their simulation and interaction using explicit finite-difference methods.

Findings

Electromagnetic solitons can exist in vacuum with model correction.

Finite-difference simulations successfully reproduce soliton interactions.

Classical dispersion effects are observed in photon passage simulations.

Abstract

A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on an explicit finite-difference technique. The experiments in two dimensions simulate travelling solitary electromagnetic waves, and show their interaction with conductive walls. In particular, the classical dispersion, exhibited by the passage of a photon through a small aperture, is examined.