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Delayed reflection of the energy flow at a potential step for dispersive wave packets
Author(s) -
Ali Mehmeti F.,
Régnier V.
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.484
Subject(s) - mathematics , reflection (computer programming) , wave packet , energy (signal processing) , mathematical analysis , transmission (telecommunications) , flow (mathematics) , network packet , constant (computer programming) , dispersion relation , point (geometry) , energy flow , dispersion (optics) , signal (programming language) , optics , geometry , physics , quantum mechanics , telecommunications , statistics , computer science , computer network , programming language
We study Klein–Gordon equations with constant coefficients and different dispersion relations on two one‐dimensional semi‐infinite media coupled with transmission conditions. We obtain lower and upper bounds of the reflected part of the energy flow at the connecting point when the frequency band involved in the initial signal is sufficiently narrow. We detect a phenomenon of delayed reflection for low frequency wave packets, which is in accordance with the recent experiments of Haibel and Nimtz. The result is then generalized for a star‐shaped network of n semi‐infinite branches connected at one point. Copyright © 2004 John Wiley & Sons, Ltd.