TY - JOUR
T1 - On Short Wave-Long Wave Interactions in the Relativistic Context
AU - Dias , João Paulo
AU - Frid , Hermano
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 263
EP - 284
PY - 2022
DA - 2022/03
SN - 1
DO - http://doi.org/10.4208/cmaa.2021-0006
UR - https://global-sci.org/intro/article_detail/cmaa/20308.html
KW - Short wave-long wave interaction, Dirac equation, Klein-Gordon equation, relativistic Burgers equation, ABI equations.
AB - <p style="text-align: justify;">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.</p>