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

Te-Sheng Lin, D. Tseluiko, M. G. Blyth*, S. Kalliadasis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)291-297
Number of pages7
JournalApplied Mathematics Letters
StatePublished - 1 Dec 2018


  • Evolution equation
  • Long-wave model
  • Numerical continuation

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