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Control methods for localization of nonlinear waves. / Porubov, Alexey; Andrievsky, Boris.

In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 375, No. 2088, 20160212, 06.03.2017.

Research output: Contribution to journal › Article › peer-review

Harvard

Porubov, A & Andrievsky, B 2017, 'Control methods for localization of nonlinear waves', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 375, no. 2088, 20160212. https://doi.org/10.1098/rsta.2016.0212

APA

Porubov, A., & Andrievsky, B. (2017). Control methods for localization of nonlinear waves. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375(2088), [20160212]. https://doi.org/10.1098/rsta.2016.0212

Vancouver

Porubov A, Andrievsky B. Control methods for localization of nonlinear waves. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2017 Mar 6;375(2088). 20160212. https://doi.org/10.1098/rsta.2016.0212

Author

Porubov, Alexey ; Andrievsky, Boris. / Control methods for localization of nonlinear waves. In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2017 ; Vol. 375, No. 2088.

BibTeX

@article{c7bb54278100453d8438707a49175978,
title = "Control methods for localization of nonlinear waves",
abstract = "A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.",
keywords = "Feedback control, Nonlinear wave, Numerical solution",
author = "Alexey Porubov and Boris Andrievsky",
year = "2017",
month = mar,
day = "6",
doi = "10.1098/rsta.2016.0212",
language = "English",
volume = "375",
journal = "Philosophical transactions. Series A, Mathematical, physical, and engineering sciences",
issn = "0962-8428",
publisher = "Royal Society of London",
number = "2088",

}

RIS

TY - JOUR

T1 - Control methods for localization of nonlinear waves

AU - Porubov, Alexey

AU - Andrievsky, Boris

PY - 2017/3/6

Y1 - 2017/3/6

N2 - A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.

AB - A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.

KW - Feedback control

KW - Nonlinear wave

KW - Numerical solution

UR - http://www.scopus.com/inward/record.url?scp=85011032490&partnerID=8YFLogxK

U2 - 10.1098/rsta.2016.0212

DO - 10.1098/rsta.2016.0212

M3 - Article

C2 - 28115609

AN - SCOPUS:85011032490

VL - 375

JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

SN - 0962-8428

IS - 2088

M1 - 20160212

ER -

ID: 41250590