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

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journal contribution
posted on 19.11.2018, 11:27 by Te-Sheng Lin, Dmitri 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.

Funding

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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Applied Mathematics Letters

Volume

86

Pages

291 - 297

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.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This 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/

Acceptance date

28/06/2018

Publication date

2018

Notes

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.

ISSN

0893-9659

eISSN

1873-5452

Language

en

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