Analytic iteration procedure for solitons and traveling wavefronts with sources

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Analytic iteration procedure for solitons and traveling wavefronts with sources. / Berx, Jonas; Indekeu, Joseph O.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 38, 38LT01, 26.08.2019.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Berx, J & Indekeu, JO 2019, 'Analytic iteration procedure for solitons and traveling wavefronts with sources', Journal of Physics A: Mathematical and Theoretical, vol. 52, no. 38, 38LT01. https://doi.org/10.1088/1751-8121/ab3914

APA

Berx, J., & Indekeu, J. O. (2019). Analytic iteration procedure for solitons and traveling wavefronts with sources. Journal of Physics A: Mathematical and Theoretical, 52(38), [38LT01]. https://doi.org/10.1088/1751-8121/ab3914

Vancouver

Berx J, Indekeu JO. Analytic iteration procedure for solitons and traveling wavefronts with sources. Journal of Physics A: Mathematical and Theoretical. 2019 Aug 26;52(38). 38LT01. https://doi.org/10.1088/1751-8121/ab3914

Author

Berx, Jonas ; Indekeu, Joseph O. / Analytic iteration procedure for solitons and traveling wavefronts with sources. In: Journal of Physics A: Mathematical and Theoretical. 2019 ; Vol. 52, No. 38.

Bibtex

@article{45a90e34c6274fc2a641336165f298ed,
title = "Analytic iteration procedure for solitons and traveling wavefronts with sources",
abstract = "A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed beyond-linear-use-of-equation-superposition function method is shown to converge for nonlinear ordinary differential equations. Case studies are presented for solitary wave solutions of the Camassa-Holm equation and for traveling wavefront solutions of the Burgers equation, with source terms. The convergence of the analytical approximations towards the numerically exact solution is exponentially rapid. In practice, the zeroth-order approximation (a simple convolution) is already useful and the first-order approximation is already accurate while still easy to calculate. The type of nonlinearity can be chosen rather freely, which makes the method generally applicable.",
keywords = "analytic iteration procedure, Green s function, nonlinear differential equation, solitary wave, traveling wavefront",
author = "Jonas Berx and Indekeu, {Joseph O.}",
note = "Publisher Copyright: {\textcopyright} 2019 IOP Publishing Ltd.",
year = "2019",
month = aug,
day = "26",
doi = "10.1088/1751-8121/ab3914",
language = "English",
volume = "52",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "Institute of Physics Publishing Ltd",
number = "38",

}

RIS

TY - JOUR

T1 - Analytic iteration procedure for solitons and traveling wavefronts with sources

AU - Berx, Jonas

AU - Indekeu, Joseph O.

N1 - Publisher Copyright: © 2019 IOP Publishing Ltd.

PY - 2019/8/26

Y1 - 2019/8/26

N2 - A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed beyond-linear-use-of-equation-superposition function method is shown to converge for nonlinear ordinary differential equations. Case studies are presented for solitary wave solutions of the Camassa-Holm equation and for traveling wavefront solutions of the Burgers equation, with source terms. The convergence of the analytical approximations towards the numerically exact solution is exponentially rapid. In practice, the zeroth-order approximation (a simple convolution) is already useful and the first-order approximation is already accurate while still easy to calculate. The type of nonlinearity can be chosen rather freely, which makes the method generally applicable.

AB - A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed beyond-linear-use-of-equation-superposition function method is shown to converge for nonlinear ordinary differential equations. Case studies are presented for solitary wave solutions of the Camassa-Holm equation and for traveling wavefront solutions of the Burgers equation, with source terms. The convergence of the analytical approximations towards the numerically exact solution is exponentially rapid. In practice, the zeroth-order approximation (a simple convolution) is already useful and the first-order approximation is already accurate while still easy to calculate. The type of nonlinearity can be chosen rather freely, which makes the method generally applicable.

KW - analytic iteration procedure

KW - Green s function

KW - nonlinear differential equation

KW - solitary wave

KW - traveling wavefront

UR - http://www.scopus.com/inward/record.url?scp=85072341455&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ab3914

DO - 10.1088/1751-8121/ab3914

M3 - Journal article

AN - SCOPUS:85072341455

VL - 52

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 38

M1 - 38LT01

ER -

ID: 371847792