Standard

Localization of the sine-Gordon equation solutions. / Porubov, A. V.; Fradkov, A. L.; Bondarenkov, R. S.; Andrievsky, B. R.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 39, 10.2016, p. 29-37.

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

Harvard

Porubov, AV, Fradkov, AL, Bondarenkov, RS & Andrievsky, BR 2016, 'Localization of the sine-Gordon equation solutions', Communications in Nonlinear Science and Numerical Simulation, vol. 39, pp. 29-37. https://doi.org/10.1016/j.cnsns.2016.02.043

APA

Porubov, A. V., Fradkov, A. L., Bondarenkov, R. S., & Andrievsky, B. R. (2016). Localization of the sine-Gordon equation solutions. Communications in Nonlinear Science and Numerical Simulation, 39, 29-37. https://doi.org/10.1016/j.cnsns.2016.02.043

Vancouver

Porubov AV, Fradkov AL, Bondarenkov RS, Andrievsky BR. Localization of the sine-Gordon equation solutions. Communications in Nonlinear Science and Numerical Simulation. 2016 Oct;39:29-37. https://doi.org/10.1016/j.cnsns.2016.02.043

Author

Porubov, A. V. ; Fradkov, A. L. ; Bondarenkov, R. S. ; Andrievsky, B. R. / Localization of the sine-Gordon equation solutions. In: Communications in Nonlinear Science and Numerical Simulation. 2016 ; Vol. 39. pp. 29-37.

BibTeX

@article{01d5e18ce21e4a8cb459258904737779,
title = "Localization of the sine-Gordon equation solutions",
abstract = "Localization of the waves of the sine-Gordon equation depends on the shape of the initial condition. It is shown how initially motionless Gaussian distribution may be modified to obtain propagation of localized waves in both directions. However, the resulting localized wave profile is described neither by an asymptotic envelope-wave solution to the sine-Gordon equation nor by its exact traveling breather solution. The distributed control algorithms are developed to achieve wave localization independent of the shape of the initial condition. It is shown that localization of the waves in both directions is achieved by means of a feedforward (nonfeedback) control. The waves are similar to the envelope wave solution. The feedback distributed algorithm is shown to provide both localized waves according to analytical solutions and their unidirectional propagation. (C) 2016 Elsevier B.V. All rights reserved.",
keywords = "Feedback control, Nonlinear wave, Nonlinear equation, Numerical solution, FEEDBACK, STABILIZATION, WAVES",
author = "Porubov, {A. V.} and Fradkov, {A. L.} and Bondarenkov, {R. S.} and Andrievsky, {B. R.}",
year = "2016",
month = oct,
doi = "10.1016/j.cnsns.2016.02.043",
language = "Английский",
volume = "39",
pages = "29--37",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Localization of the sine-Gordon equation solutions

AU - Porubov, A. V.

AU - Fradkov, A. L.

AU - Bondarenkov, R. S.

AU - Andrievsky, B. R.

PY - 2016/10

Y1 - 2016/10

N2 - Localization of the waves of the sine-Gordon equation depends on the shape of the initial condition. It is shown how initially motionless Gaussian distribution may be modified to obtain propagation of localized waves in both directions. However, the resulting localized wave profile is described neither by an asymptotic envelope-wave solution to the sine-Gordon equation nor by its exact traveling breather solution. The distributed control algorithms are developed to achieve wave localization independent of the shape of the initial condition. It is shown that localization of the waves in both directions is achieved by means of a feedforward (nonfeedback) control. The waves are similar to the envelope wave solution. The feedback distributed algorithm is shown to provide both localized waves according to analytical solutions and their unidirectional propagation. (C) 2016 Elsevier B.V. All rights reserved.

AB - Localization of the waves of the sine-Gordon equation depends on the shape of the initial condition. It is shown how initially motionless Gaussian distribution may be modified to obtain propagation of localized waves in both directions. However, the resulting localized wave profile is described neither by an asymptotic envelope-wave solution to the sine-Gordon equation nor by its exact traveling breather solution. The distributed control algorithms are developed to achieve wave localization independent of the shape of the initial condition. It is shown that localization of the waves in both directions is achieved by means of a feedforward (nonfeedback) control. The waves are similar to the envelope wave solution. The feedback distributed algorithm is shown to provide both localized waves according to analytical solutions and their unidirectional propagation. (C) 2016 Elsevier B.V. All rights reserved.

KW - Feedback control

KW - Nonlinear wave

KW - Nonlinear equation

KW - Numerical solution

KW - FEEDBACK

KW - STABILIZATION

KW - WAVES

U2 - 10.1016/j.cnsns.2016.02.043

DO - 10.1016/j.cnsns.2016.02.043

M3 - статья

VL - 39

SP - 29

EP - 37

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -

ID: 13719858