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Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

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Abstract.

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

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Authors and Affiliations

  1. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    T. C. Kofane & M. Fokou

  2. Centre d’Excellence Africain en Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    T. C. Kofane, M. Fokou & A. Mohamadou

  3. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Maroua, P. O. Box 814, Maroua, Cameroon

    A. Mohamadou

  4. Department of Mathematics, California State University-Northridge, 91330-8313, Northridge, CA, USA

    E. Yomba

Authors
  1. T. C. Kofane
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  2. M. Fokou
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  3. A. Mohamadou
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  4. E. Yomba
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Correspondence to M. Fokou.

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Kofane, T.C., Fokou, M., Mohamadou, A. et al. Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation. Eur. Phys. J. Plus 132, 465 (2017). https://doi.org/10.1140/epjp/i2017-11747-6

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  • DOI: https://doi.org/10.1140/epjp/i2017-11747-6

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