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Nonlinear Dynamics

, Volume 96, Issue 4, pp 2463–2473 | Cite as

Fission and fusion collision of high-order lumps and solitons in a \((3+1)\)-dimensional nonlinear evolution equation

  • Wei LiuEmail author
  • Xiaoxiao Zheng
  • Chu Wang
  • Shengqi Li
Original Paper

Abstract

Multiple dark soliton solutions and semi-rational solutions to a \((3+1)\)-dimensional nonlinear evolution equation are obtained by a combination of the Kadomtsev–Petviashvili hierarchy reduction method and the Hirota’s bilinear method. The collision phenomena of fission and fusion of high-order lumps and solitons in the \((3+1)\)-dimensional nonlinear evolution equation are described by these semi-rational solutions. After the collision of higher-order lumps and solitons, the lumps would fuse into or fissure from the line solitons. As lumps are created or annihilated, the exchange of energy occurs between the lumps and the line solitons.

Keywords

(3+1)-Dimensional nonlinear evolution Hirota bilinear method Lump–soliton solution KP hierarchy reduction method 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11801321.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Mathematic and Information ScienceShandong Technology and Business UniversityYantaiPeople’s Republic of China
  2. 2.School of Mathematical SciencesQufu Normal UniversityQufuPeople’s Republic of China

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