Multi-wave, breather wave and lump solutions of the Boiti-Leon-Manna-Pempinelli equation with variable coefficients

TL;DR

This paper derives various exact solutions, including multi-wave, breather, and lump solutions, for a variable-coefficient Boiti-Leon-Manna-Pempinelli equation, enhancing understanding of fluid dynamics.

Contribution

It introduces new solution methods for the variable-coefficient equation using three different analytical approaches, expanding the solution set for this class of equations.

Findings

Obtained multi-wave, breather, and lump solutions

Verified solutions with Mathematica software

Analyzed propagation characteristics through 3D visualization

Abstract

In this paper, a variable-coefficient Boiti-Leon-Manna-Pempinelli equation is to be investigated. We obtain abundant multi-wave, breather wave and lump solutions by using the three waves method, the homoclinic breather approach and the Hirota's bilinear method. All solutions have been verified to be correct with the help of Mathematica software. We study the propagation characteristics of these solutions by some three-dimensional images. The obtained results are useful for understanding fluid propagating and incompressible fluid.