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Generalised Camassa–Holm–Kadomtsev–Petviashvili equation; Kadomtsev–Petviashvili– Benjamin–Bona–Mahony equation; generalised exponential rational function method; simplest equation method

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.

BEHZAD GHANBARI^{1 2} JIAN-GUO LIU³

1. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran
2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahçe¸sehir University, P.O. Box 34349, Istanbul, Turkey
3. College of Computer, Jiangxi University of Traditional Chinese Medicine, Jiangxi 330004, China

Published

10 January 2020

Manuscript received

7 August 2019

Manuscript revised

11 September 2019

Accepted

17 October 2019

Early published

Unedited version published online

Final version published online

3 January 2020