Nonlinear Dynamics

, Volume 95, Issue 2, pp 1027–1033 | Cite as

Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev–Petviashvili equation

  • Jian-Guo LiuEmail author
  • Mostafa Eslami
  • Hadi Rezazadeh
  • Mohammad Mirzazadeh
Original Paper


In this work, a non-isospectral and variable-coefficient Kadomtsev–Petviashvili equation is considered using Hirota’s bilinear form and a direct assumption with arbitrary functions. Analytical rational solutions in light of positive quadratic functions and lump solutions of the variable-coefficient Kadomtsev–Petviashvili equation are obtained. These lump solutions describe two types of characters by some three-dimensional graphs and contour plots, which contain bright lump wave and bright–dark lump wave. Meanwhile, periodic structure of the lump wave is also shown.


Rational solutions Lump solutions Variable-coefficient Kadomtsev–Petviashvili equation Hirota’s bilinear form 


Compliance with ethical standards

Conflict of interests

The authors declare that there are no conflict of interests regarding the publication of this article.

Ethical standards

The authors state that this research complies with ethical standards. This research does not involve either human participants or animals.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of ComputerJiangxi University of Traditional Chinese MedicineJiangxiChina
  2. 2.School of scienceBeijing University of Posts and TelecommunicationsBeijingChina
  3. 3.Department of Mathematics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran
  4. 4.Faculty of Engineering TechnologyAmol University of Special Modern TechnologiesAmolIran
  5. 5.Department of Engineering Sciences, Faculty of Technology and Engineering, East of GuilanUniversity of GuilanRudsar-VajargahIran

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