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

Te-Sheng Lin; Dmitri Tseluiko; Mark G. Blyth; Serafim Kalliadasis

doi:10.1016/j.aml.2018.06.034

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

Te-Sheng Lin, Dmitri Tseluiko, Mark G. Blyth, Serafim Kalliadasis

Fluids & Structures

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

5 Citations (Scopus)

22 Downloads (Pure)

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 the 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
Early online date	7 Jul 2018
DOIs	https://doi.org/10.1016/j.aml.2018.06.034
Publication status	Published - Dec 2018

Keywords

numerical continuation
evolution equation
long-wave model

Access to Document

10.1016/j.aml.2018.06.034

Accepted manuscriptAccepted author manuscript, 999 KBLicence: CC BY-NC-ND

The Mathematics of Multilayer Microfluidics: Analysis, Hybrid Modelling and Novel Simulations Underpinning New Technologies at the Microscale.
Blyth, M., Papageorgiou, D., Crowdy, D. & Tseluiko, D.
Engineering and Physical Sciences Research Council
1/02/14 → 31/01/17
Project: Research

Cite this

@article{0612474631a745b5bbd30cbea57379a0,

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 the 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 = "numerical continuation, evolution equation, long-wave model",

author = "Te-Sheng Lin and Dmitri Tseluiko and Blyth, {Mark G.} and Serafim Kalliadasis",

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",

publisher = "Elsevier",

}

TY - JOUR

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

AU - Lin, Te-Sheng

AU - Tseluiko, Dmitri

AU - Blyth, Mark G.

AU - Kalliadasis, Serafim

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 the 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 the 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 - numerical continuation

KW - evolution equation

KW - long-wave model

U2 - 10.1016/j.aml.2018.06.034

DO - 10.1016/j.aml.2018.06.034

M3 - Article

VL - 86

SP - 291

EP - 297

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -

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

Abstract

Keywords

Access to Document

Projects

The Mathematics of Multilayer Microfluidics: Analysis, Hybrid Modelling and Novel Simulations Underpinning New Technologies at the Microscale.

Cite this