Complexitons, Bilinear forms and Bilinear Bäcklund transformation of a [formula omitted]-dimensional Boiti–Leon–Manna–Pempinelli model describing incompressible fluid

Abstract

In this work, we have presented bilinear form and two separate Bäcklund transformations (BT) for a (2+1)-Dimensional Bilti–Leon–Manna–Pempinelli equation (BLMPE), which characterizes the flow of an incompressible fluid and demonstrates the development of the horizontal velocity component of water waves that propagate in the XY plane in an infinite narrow passage of constant depth. The first form includes six arbitrary parameters, but the second version has only two. Based on the suggested bilinear (BT), rational traveling wave solutions with random wave numbers and classifications of exponential are determined. Furthermore, the extended transformed rational function approach, using the Hirota bilinear version of the governing model, is employed to provide complexions. We have also given the 3D and 2D graphics of the obtained solutions to understand the physical dynamics of the BLMPE.