Analysis and Mathematical Physics

, Volume 9, Issue 4, pp 2329–2344 | Cite as

Abundant exact solutions and interaction phenomena of the (2 + 1)-dimensional YTSF equation

  • Si-Jia Chen
  • Yu-Hang Yin
  • Wen-Xiu MaEmail author
  • Xing LüEmail author


In this paper, we study abundant exact solutions including the lump and interaction solutions to the (2 + 1)-dimensional Yu–Toda–Sasa–Fukuyama equation. With symbolic computation, lump solutions and the interaction solutions are generated directly based on the Hirota bilinear formulation. Analyticity and well-definedness is guaranteed through some conditions posed on the parameters. With special choices of the involved parameters, the interaction phenomena are simulated and discussed. We find the lump moves from one hump to the other hump of the two-soliton, while the lump separates from the hump of the one-soliton.


Hirota bilinear form Lump solutions Interaction solutions YTSF equation 



This work is supported by the National Natural Science Foundation of China under Grant No. 71971015, and the Fundamental Research Funds for the Central Universities of China (2018RC031). Y. H. Yin is supported by the Project of National Innovation and Entrepreneurship Training Program for College Students under Grant No. 201710004054.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiao Tong UniversityBeijingChina
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  3. 3.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  4. 4.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  5. 5.Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical ModellingNorth-West UniversityMmabathoSouth Africa

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