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
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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