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Title: Continuation methods for time-periodic travelling-wave solutions to evolution equations
Authors: Lin, Te-Sheng
Tseluiko, Dmitri
Blyth, Mark G.
Kalliadasis, Serafim
Keywords: Numerical continuation
Evolution equation
Long-wave model
Issue Date: 2018
Publisher: © Elsevier
Citation: LIN, T-S. ... et al., 2018. Continuation methods for time-periodic travelling-wave solutions to evolution equations. Applied Mathematics Letters, 86, pp. 291-297.
Abstract: © 2018 Elsevier Ltd 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.
Description: This paper was accepted for publication in the journal Applied Mathematics Letters and the definitive published version is available at https://doi.org/10.1016/j.aml.2018.06.034.
Sponsor: We acknowledge financial support by the EPSRC under grants EP/J001740/1 and EP/K041134/1 and by the Ministry of Science and Technology of Taiwan under research grant MOST-103-2115-M-009-015-MY2.
Version: Accepted for publication
DOI: 10.1016/j.aml.2018.06.034
URI: https://dspace.lboro.ac.uk/2134/36058
Publisher Link: https://doi.org/10.1016/j.aml.2018.06.034
ISSN: 0893-9659
Appears in Collections:Published Articles (Maths)

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