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Volume 1, Issue 2
On Short Wave-Long Wave Interactions in the Relativistic Context

João Paulo Dias & Hermano Frid

DOI: 10.4208/cmaa.2021-0006

Commun. Math. Anal. Appl., 1 (2022), pp. 263-284.

Published online: 2022-03

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  • 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.

  • Keywords

Short wave-long wave interaction, Dirac equation, Klein-Gordon equation, relativistic Burgers equation, ABI equations.

  • AMS Subject Headings

35L65, 35Q41, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-1-263, author = {Dias , João Paulo and Frid , Hermano}, title = {On Short Wave-Long Wave Interactions in the Relativistic Context}, journal = {Communications in Mathematical Analysis and Applications}, year = {2022}, volume = {1}, number = {2}, pages = {263--284}, 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.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2021-0006}, url = {http://global-sci.org/intro/article_detail/cmaa/20308.html} }
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 -

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.

Dias , João Paulo and Frid , Hermano. (2022). On Short Wave-Long Wave Interactions in the Relativistic Context. Communications in Mathematical Analysis and Applications. 1 (2). 263-284. doi:10.4208/cmaa.2021-0006
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