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

Lin, Te-Sheng, Tseluiko, Dmitri, Blyth, Mark G. and Kalliadasis, Serafim (2018) Continuation methods for time-periodic travelling-wave solutions to evolution equations. Applied Mathematics Letters, 86. pp. 291-297. ISSN 0893-9659

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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.

Item Type: Article
Uncontrolled Keywords: numerical continuation,evolution equation,long-wave model
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: LivePure Connector
Date Deposited: 03 Jul 2018 10:30
Last Modified: 22 Apr 2020 06:46
URI: https://ueaeprints.uea.ac.uk/id/eprint/67498
DOI: 10.1016/j.aml.2018.06.034

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