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Bilinear representations and lump-type waves for a fifth-order nonlinear wave equation

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Abstract.

In this work, we study a fifth-order nonlinear wave equation. By using the proper transformation and auxiliary parameter, two different bilinear representations are presented. We also derive a bilinear Bäcklund transformation, a Lax pair and lump-type wave solutions. The dynamics of lump-type wave solutions are investigated and exhibited mathematically and graphically. We further investigate the interaction between a kink-type solitary wave and a lump-type wave. Absorb and emit interactions between two types of solitary wave solutions are presented.

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Authors and Affiliations

  1. Department of Mathematics, Kunming University of Science and Technology, 650500, Kunming, China

    Yuefeng Zhou, Chuanjian Wang, Xingyong Zhang & Hui Fang

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  1. Yuefeng Zhou
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  2. Chuanjian Wang
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  3. Xingyong Zhang
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  4. Hui Fang
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Correspondence to Chuanjian Wang.

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Zhou, Y., Wang, C., Zhang, X. et al. Bilinear representations and lump-type waves for a fifth-order nonlinear wave equation. Eur. Phys. J. Plus 134, 569 (2019). https://doi.org/10.1140/epjp/i2019-13083-3

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  • DOI: https://doi.org/10.1140/epjp/i2019-13083-3

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