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Interaction solutions for a reduced extended \(\mathbf{(3}\varvec{+}{} \mathbf{1)}\)-dimensional Jimbo–Miwa equation

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Abstract

In this paper, the exact solutions of a reduced extended \((3+1)\)-dimensional Jimbo–Miwa equation are investigated with the help of its bilinear representation and symbolic computation. Firstly, a kind of bright–dark lump wave solutions is directly obtained by taking the solution F in bilinear equation as a quadratic function. Furthermore, the interaction solutions between one lump wave and one stripe wave are also presented by taking F as a combination of quadratic function and exponential function. Finally, by taking F as a combination of quadratic function and hyperbolic cosine function, the rogue wave which aroused by the interaction between lump soliton and a pair of stripe solitons are obtained. The dynamic properties of the above three kinds of exact solutions are displayed vividly by figures.

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Acknowledgements

The authors would like to express their sincere thanks to the referees for their valuable comments. This work is supported by the National Natural Science Foundation of China (Nos. 11405103, 11571008, 51679132, 11601321 and 11526137), and the Shanghai Science and Technology Committee (No. 17040501600).

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Authors and Affiliations

  1. College of Art and Sciences, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China

    Yun-Hu Wang, Hui Wang & Chaolu Temuer

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Yun-Hu Wang

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

    Huan-He Dong

  4. College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China

    Hong-Sheng Zhang

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  1. Yun-Hu Wang
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  2. Hui Wang
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  3. Huan-He Dong
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  4. Hong-Sheng Zhang
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  5. Chaolu Temuer
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Correspondence to Yun-Hu Wang or Hui Wang.

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Wang, YH., Wang, H., Dong, HH. et al. Interaction solutions for a reduced extended \(\mathbf{(3}\varvec{+}{} \mathbf{1)}\)-dimensional Jimbo–Miwa equation. Nonlinear Dyn 92, 487–497 (2018). https://doi.org/10.1007/s11071-018-4070-z

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  • DOI: https://doi.org/10.1007/s11071-018-4070-z

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