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Analysis and Mathematical Physics

, Volume 9, Issue 3, pp 1511–1523 | Cite as

Lump-type solutions and interaction solutions in the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

  • Min-Jie Dong
  • Shou-Fu TianEmail author
  • Xiu-Bin Wang
  • Tian-Tian ZhangEmail author
Article

Abstract

In this work, we consider the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. By employing the extended homoclininc test approach and Hirota bilinear method, we derive a class of lump solutions of the potential YTSF equation. It is interesting that interaction solutions between the lump-type solution and one stripe soliton, and the lump-type solution and a pair of resonance solution are obtained, respectively, by using a direct method. The interaction solutions of the potential YTSF equation show that a lump-type solution appears from a soliton wave and swallowed by it later, which are the completely non-elastic interactions that rare to see. Moreover, we also obtain its periodic lump-type solutions. It is hoped that our results can be used to enrich the dynamic behaviors of the YTSF-type equations.

Keywords

The (3 + 1)-dimensional potential YTSF equation Hirota bilinear method Lump-type solutions 

Mathematics Subject Classification

35Q51 35Q53 35C99 68W30 74J35 

Notes

Acknowledgements

We express our sincere thanks to the Editor and the Referees for their valuable comments. This work was supported by the Jiangsu Province Natural Science Foundation of China under Grant No. BK20181351, the Postgraduate Research and Practice Program of Education and Teaching Reform of CUMT under Grant No. YJSJG_2018_036, the “Qinglan Engineering project” of Jiangsu Universities, the National Natural Science Foundation of China under Grant No. 11301527, the Fundamental Research Fund for the Central Universities under the Grant No. 2017XKQY101, and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematics and Institute of Mathematical PhysicsChina University of Mining and TechnologyXuzhouPeople’s Republic of China

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