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Hybrid solitary waves for the generalized Kuramoto-Sivashinsky equation

Abstract.

The generalized Kuramoto-Sivashinsky equation is considered. The Bogning-Djeumen Tchaho-Kofané method is used to study approximate solitary wave solutions of this equation. It is shown that the generalized Kuramoto-Sivashinsky equation has hybrid solitary wave solutions which are a combination of bright, kink, and dark solitary wave profiles, respectively. The possibility to alter the amplitude of each individual solitary wave of the combination allows to choose which profiles are dominant. Numerical simulations corroborate the analytical predictions with a good accuracy. Further numerical simulations reveal that the hybrid solitary wave solutions taken as a perturbation of the trivial solution remain stable for a relatively long time, hence might be observed in experiments.

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Djeumen Tchaho, C.T., Omanda, H.M. & Belobo Belobo, D. Hybrid solitary waves for the generalized Kuramoto-Sivashinsky equation. Eur. Phys. J. Plus 133, 387 (2018). https://doi.org/10.1140/epjp/i2018-12218-4

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  • DOI: https://doi.org/10.1140/epjp/i2018-12218-4