Complexiton and resonant multi-solitons of a (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

This work is concerned with the extraction of auto-Bäcklund transformations of (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in accordance with the extended homogeneous balance (HB) method incorporating Maple. Subsequently, these transformations are used to study analytic explicit solutions of this equation. Also, based on the Hirota bilinear form and the extended transformed rational function method, complexiton solutions have been found of the (4 + 1)-dimensional BLMP equation through a direct symbolic computation with Maple. This method is the improved form of the transformed rational function method. The obtained complexiton solutions, including trigonometric and hyperbolic trigonometric solutions, have been verified utilizing Hirota bilinear forms. Some of the solutions are depicted in 3D graphs to understand physical properties. The reported results are new and have applications in several scientific fields such as incompressible fluids.