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Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded domain

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Abstract

The main goal of this paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded domain near a change of bifurcation, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation, which is called the Ginzburg-Landau (G-L for short) equation, for the amplitudes of the dominating modes.

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Acknowledgments

The authors would like to express their sincere thanks to the referees for helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

    Wael W. Mohammed

  2. Department of Mathematics, Faculty of Science, Hail University, Hail, Saudi Arabia

    Wael W. Mohammed

Authors
  1. Wael W. Mohammed
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Correspondence to Wael W. Mohammed.

Additional information

This work was supported by the Deanship of Scientific Research, University of Hail, KSA (No. 0150258).

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Mohammed, W.W. Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded domain. Chin. Ann. Math. Ser. B 39, 145–162 (2018). https://doi.org/10.1007/s11401-018-1057-5

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  • DOI: https://doi.org/10.1007/s11401-018-1057-5

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