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

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.