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Feedback control for some solutions of the sine-Gordon equation

Authors :
Alexey V. Porubov
Alexander L. Fradkov
Boris Andrievsky
Source :
Applied Mathematics and Computation. 269:17-22
Publication Year :
2015
Publisher :
Elsevier BV, 2015.

Abstract

Evolution of an initial localized bell-shaped state for the sine-Gordon equation is considered. It is obtained numerically that variation in the parameters of the localized input gives rise to different propagating waves as time goes. The speed gradient feedback control method is employed to achieve unified wave profile weakly dependent on initial conditions. Two speed-gradient like algorithms are developed and compared. It is shown that the algorithm using coefficient at the second spatial derivative term in the sine-Gordon equation allows one to generate the same wave with prescribed energy from different initial states having different energies.

Details

ISSN :
00963003
Volume :
269
Database :
OpenAIRE
Journal :
Applied Mathematics and Computation
Accession number :
edsair.doi...........9ab278b1a4ce7a169f86dc7e2894e298
Full Text :
https://doi.org/10.1016/j.amc.2015.07.040