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Hybrid solitary waves for the generalized Kuramoto-Sivashinsky equation

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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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Authors and Affiliations

  1. African Centre for Advanced Studies, P.O. Box 4477, Yaounde, Cameroon

    C. T. Djeumen Tchaho, H. M. Omanda & D. Belobo Belobo

  2. Lycée Technique Fulbert Bongotha, P.O. Box 15, Moanda, Gabon

    C. T. Djeumen Tchaho

  3. Laboratoire Pluridisciplinaire des Sciences, Ecole Normale Supérieure, P.O. Box 17009, Libreville, Gabon

    H. M. Omanda

  4. PREPAVOGT, P.O. Box 765, Yaounde, Cameroon

    D. Belobo Belobo

Authors
  1. C. T. Djeumen Tchaho
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  2. H. M. Omanda
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  3. D. Belobo Belobo
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Correspondence to D. Belobo Belobo.

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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

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