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Exact solitary wave solutions to the (2 + 1)-dimensional generalised Camassa–Holm–Kadomtsev–Petviashvili equation

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Abstract

In this paper, a (\(2{+}1\))-dimensional nonlinear evolution equation (NLEE), namely the generalised Camassa–Holm–Kadomtsev–Petviashvili equation (gCHKP) or Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation (KP-BBM), is examined. After applying the newly developed generalised exponential rational function method (GERFM), 14 travelling wave solutions are formally generated. It is worth mentioning that by specifying values to free parameters some previously obtained solutions can be recovered. The simplest equation method (SEM) is used to prove that the solutions obtained by GERFM are good. With the aid of a symbolic computation system, we prove that GERFM is more efficient and faster.

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Acknowledgements

The authors would like to thank the referees for their valuable comments which improved the paper. The work of the second author is supported by the Science and Technology project of Jiangxi Provincial Health and Family Planning Commission (20175537).

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Authors and Affiliations

  1. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran

    Behzad Ghanbari

  2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahçeşehir University, P.O. Box 34349, Istanbul, Turkey

    Behzad Ghanbari

  3. College of Computer, Jiangxi University of Traditional Chinese Medicine, Jiangxi, 330004, China

    Jian-Guo Liu

Authors
  1. Behzad Ghanbari
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  2. Jian-Guo Liu
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Corresponding author

Correspondence to Jian-Guo Liu.

Appendix: Maple code

Appendix: Maple code

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Ghanbari, B., Liu, JG. Exact solitary wave solutions to the (2 + 1)-dimensional generalised Camassa–Holm–Kadomtsev–Petviashvili equation. Pramana - J Phys 94, 21 (2020). https://doi.org/10.1007/s12043-019-1893-1

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  • DOI: https://doi.org/10.1007/s12043-019-1893-1

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