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On the interaction of NLS‐described modulating pulses with different carrier waves
Author(s) -
ChirilusBruckner Martina,
Schneider Guido,
Uecker Hannes
Publication year - 2007
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.884
Subject(s) - pulse (music) , nonlinear system , carrier signal , mathematics , nonlinear schrödinger equation , statement (logic) , order (exchange) , schrödinger equation , mathematical analysis , physics , optics , quantum mechanics , telecommunications , computer science , finance , transmission (telecommunications) , detector , law , political science , economics
Abstract We give a detailed analysis of the interaction of two modulating pulse solutions of a nonlinear wave equation. These solutions consist of pulse‐like envelopes satisfying approximately a nonlinear Schrödinger equation, advancing in the laboratory frame, and modulating underlying wave trains. We improve the bound for the possible shift of the envelopes caused by the interaction of two well‐prepared pulses from order (1) to order (ε). Thus, we manifest the statement that there is almost no interaction of pulses with different carrier waves. Copyright © 2007 John Wiley & Sons, Ltd.