Multi-wave complexiton, multi-wave, interaction-wave and the travelling wave solutions to the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation for the incompressible fluid

The current research aims to look into the exact solutions (ESs) of the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation (BLMPE), which describes the irrotational-incompressible fluid. The Hirota bilinear equation of the problem under consideration is developed by applying the Cole–Hopf transform. Then, the ansatz function, combined with the symbolic computation, is utilised to extract the ESs. Some new types of ESs like the multi-wave complexiton solution (MWCS), multi-wave solution (MWS) and the interaction wave solution (IWS) are successfully constructed. Furthermore, ESs such as the travelling wave solution (TWS) are also explored via the modified Kudryashov method. The dynamic characteristics of the ESs are described graphically using the Mathematica software and their physical explanations are presented. Compared with the publicly available literature, the obtained ESs are all new and have not yet been reported. The ideas in this work can be used to investigate the ESs of the other PDEs that appear in physics.