Self-similar shock wave solutions of the non-linear Maxwell equations

TL;DR

This paper investigates self-similar solutions to nonlinear Maxwell equations with power-law permittivity and permeability, revealing shock-wave phenomena and localized solutions relevant to high-intensity laser-matter interactions.

Contribution

It introduces a novel analysis of self-similar shock-wave solutions in nonlinear Maxwell equations with power-law dependencies, highlighting potential physical phenomena in complex materials.

Findings

Existence of electromagnetic shock-wave solutions

Discovery of localized solutions with compact support

Relevance to high-intensity laser experiments

Abstract

In our study we consider nonlinear, power-law field-dependent electrical permitivity and magnetic permeability and investigate the time-dependent Maxwell equations with the self-similar Ansatz. This is a first-order hyperbolic PDE system which can conserve non-continuous initial conditions describing electromagnetic shock-waves. Besides shock-waves other interesting solutions (e.g. with localized compact support) can be found with delicate physical properties. Such phenomena may happen in complex materials induced by the planned powerful Extreme Light Infrastructure(ELI) laser pulses.