Continuation methods for time-periodic travelling-wave solutions to evolution equations

Te-Sheng Lin; D. Tseluiko; M. G. Blyth; S. Kalliadasis

doi:10.1016/j.aml.2018.06.034

Continuation methods for time-periodic travelling-wave solutions to evolution equations

Te-Sheng Lin, D. Tseluiko, M. G. Blyth^*, S. Kalliadasis

^*Corresponding author for this work

Department of Applied Mathematics

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

5 Scopus citations

Abstract

A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational symmetry. The derived system of equations allows one to follow the branch of travelling-wave solutions as well as solutions that are time-periodic in a frame of reference travelling at a constant speed. Finally, we show as an example the bifurcation and stability analysis of single and double-pulse waves in long-wave models of electrified falling films.

Original language	English
Pages (from-to)	291-297
Number of pages	7
Journal	Applied Mathematics Letters
Volume	86
DOIs	https://doi.org/10.1016/j.aml.2018.06.034
State	Published - Dec 2018

Keywords

Evolution equation
Long-wave model
Numerical continuation

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title = "Continuation methods for time-periodic travelling-wave solutions to evolution equations",

abstract = "A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational symmetry. The derived system of equations allows one to follow the branch of travelling-wave solutions as well as solutions that are time-periodic in a frame of reference travelling at a constant speed. Finally, we show as an example the bifurcation and stability analysis of single and double-pulse waves in long-wave models of electrified falling films.",

keywords = "Evolution equation, Long-wave model, Numerical continuation",

author = "Te-Sheng Lin and D. Tseluiko and Blyth, {M. G.} and S. Kalliadasis",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2018",

month = dec,

doi = "10.1016/j.aml.2018.06.034",

language = "English",

volume = "86",

pages = "291--297",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

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T1 - Continuation methods for time-periodic travelling-wave solutions to evolution equations

AU - Lin, Te-Sheng

AU - Tseluiko, D.

AU - Blyth, M. G.

AU - Kalliadasis, S.

PY - 2018/12

Y1 - 2018/12

N2 - A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational symmetry. The derived system of equations allows one to follow the branch of travelling-wave solutions as well as solutions that are time-periodic in a frame of reference travelling at a constant speed. Finally, we show as an example the bifurcation and stability analysis of single and double-pulse waves in long-wave models of electrified falling films.

AB - A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational symmetry. The derived system of equations allows one to follow the branch of travelling-wave solutions as well as solutions that are time-periodic in a frame of reference travelling at a constant speed. Finally, we show as an example the bifurcation and stability analysis of single and double-pulse waves in long-wave models of electrified falling films.

KW - Evolution equation

KW - Long-wave model

KW - Numerical continuation

UR - http://www.scopus.com/inward/record.url?scp=85050460092&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2018.06.034

DO - 10.1016/j.aml.2018.06.034

M3 - Article

AN - SCOPUS:85050460092

SN - 0893-9659

VL - 86

SP - 291

EP - 297

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Continuation methods for time-periodic travelling-wave solutions to evolution equations

Abstract

Keywords

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