On short wave-long wave interactions in the relativistic context

TL;DR

This paper develops models for short wave-long wave interactions in relativistic physics, replacing the nonlinear Schrödinger equation with a nonlinear Dirac equation, and explores two specific cases involving scalar conservation laws and electromagnetic equations.

Contribution

It introduces a novel relativistic framework for wave interactions, extending existing models to include nonlinear Dirac equations and specific physical scenarios.

Findings

Models successfully incorporate relativistic effects in wave interactions

Demonstrates applicability to scalar conservation laws and electromagnetic equations

Provides a foundation for further research in relativistic wave dynamics

Abstract

In this paper we introduce models of short wave-long wave interactions in the relativistic setting. In this context the nonlinear Schr\"odinger equation is no longer adequate for describing short waves and is replaced by a nonlinear Dirac equation. Two specific examples are considered: the case where the long waves are governed by a scalar conservation law; and the case where the long waves are governed by the augmented Born-Infeld equations in electromagnetism.