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Continuation methods for time-periodic travelling-wave solutions to evolution equations
journal contributionposted on 2018-11-19, 11:27 authored by Te-Sheng Lin, Dmitri TseluikoDmitri Tseluiko, Mark G. Blyth, Serafim Kalliadasis
© 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.
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.
- Mathematical Sciences
Published inApplied Mathematics Letters
Pages291 - 297
CitationLIN, T-S. ... et al., 2018. Continuation methods for time-periodic travelling-wave solutions to evolution equations. Applied Mathematics Letters, 86, pp. 291-297.
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis 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.