On Short Wave-Long Wave Interactions in the Relativistic Context
DOI:
https://doi.org/10.4208/cmaa.2021-0006Keywords:
Short wave-long wave interaction, Dirac equation, Klein-Gordon equation, relativistic Burgers equation, ABI equations.Abstract
In this paper we introduce models of short wave-long wave interactions in the relativistic setting. In this context the nonlinear Schrödinger 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.