Generation and Suppression of Radiation by Solitary Pulses

Hsueh-Chia Chang (), Evgeny A. Demekhin and Evgeny Kalaidin
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Hsueh-Chia Chang: University of Notre Dame, Department of Chemical Engineering
Evgeny A. Demekhin: University of Notre Dame, Department of Chemical Engineering
Evgeny Kalaidin: University of Notre Dame, Department of Chemical Engineering

A chapter in Differential Equations Theory, Numerics and Applications, 1997, pp 17-50 from Springer

Abstract: Abstract The description of the spatio-temporal dynamics of an extended active/dispersive medium can be simplified considerably if the dynamics is dominated by a fixed number of solitary pulses separated by radiation-free flat substrates. Radiation is generated in a noise-free environment when excess mass drains out of a pulse in the form of a spreading shelf and the radiation grows rapidly by feeding on the active substrate. However, this growth can be suppressed if the localized radiation packet is absorbed by a second pulse. It is shown that both the generation and suppression mechanisms can be quantitatively understood by analyzing the essential spectrum and a peculiar discrete spectrum of the equilibrium pulse called resonance pole. An explicit criterion is then developed and verified numerically for when the spatio-temporal dynamics of the generalized Kuramoto-Sivashinsky (gK S) equation is dominated by robust solitary pulses.

Keywords: Zero Mode; Essential Spectrum; Fourier Mode; Speed Mode; Drainage Rate (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-5157-3_2

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DOI: 10.1007/978-94-011-5157-3_2

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