Multi-lump, resonant Y-shape soliton, complex multi kink solitons and the solitary wave solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for incompressible fluid

The major contribution in this paper is to inquire into some new exact solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) which plays a major role in area of the incompressible fluid. Taking advantage of the Cole-Hopf transform, we extract its bilinear form. Then two different kinds of the multi-lump solutions are probed by applying the new homoclinic approach. Secondly, the Y-shape soliton solutions are explored via assigning the resonance conditions to the N-soliton solutions. Additionally, the complex multi kink soliton solutions (CMKSSs) are investigated through the Hirota bilinear method. Lastly, some other wave solutions including the kink and anti-kink solitary wave solutions are developed with the aid of two efficacious approaches, namely the variational method and Kudryashov method. In the meantime, the profiles of the accomplished solutions are displayed graphically via Maple.