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Interaction phenomena between a lump and other multi-solitons for the \({\mathbf {(2+1)}}\)-dimensional BLMP and Ito equations

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Abstract

In this paper, “new” interaction solutions between a lump solution and other multi-soliton (kinky or stripe) solutions are studied through developing a “new” direct method based on the Hirota bilinear form for the \((2+1)\)-dimensional BLMP equation and the \((2+1)\)-dimensional Ito equation. Interaction solutions degenerate into lump (or kinky/stripe) solutions while the involved exponential function (or quadratic function) disappears. The interaction phenomena in the presented solutions show that a lump can be drowned or swallowed by other multi-solitary waves (kinky or stripe waves), and such interactions are very rare non-elastic collisions. What is more, we find that the positions of the interaction between a lump and three or four kinky waves are different while we choose different parameters, and the collisions may be at the bottom, middle, top or other positions. The dynamic characteristics of the constructed interaction solutions are illustrated by sequences of interesting figures plotted with the help of Maple.

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Acknowledgements

We are very grateful to the editor and reviewers for their constructive comments and suggestions. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. This research is supported by the Natural Science Basic Research Program of Shaanxi (Grant No. 2017JM1024) and sponsored by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (Grant No. ZZ2018174).

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Chunhua He, Yaning Tang & Jinli Ma

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wenxiu Ma

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Wenxiu Ma

  4. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wenxiu Ma

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  1. Chunhua He
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  2. Yaning Tang
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Correspondence to Yaning Tang.

Appendix

Appendix

See Figs. 9 and 10.

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He, C., Tang, Y., Ma, W. et al. Interaction phenomena between a lump and other multi-solitons for the \({\mathbf {(2+1)}}\)-dimensional BLMP and Ito equations. Nonlinear Dyn 95, 29–42 (2019). https://doi.org/10.1007/s11071-018-4548-8

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