  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.
