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Nonlinear Dynamics

, Volume 92, Issue 2, pp 487–497 | Cite as

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

  • Yun-Hu Wang
  • Hui Wang
  • Huan-He Dong
  • Hong-Sheng Zhang
  • Chaolu Temuer
Original Paper

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.

Keywords

Interaction solutions Lump wave solution Rogue wave solution Jimbo–Miwa equation 

Notes

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).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Art and SciencesShanghai Maritime UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China
  3. 3.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  4. 4.College of Ocean Science and EngineeringShanghai Maritime UniversityShanghaiPeople’s Republic of China

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