The present article deals with M-soliton solution of the (2+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation
by virtue of Hirota bilinear operator method. The obtained solutions for solving the current equation represent some localized
waves including soliton, periodic and cross-kink solutions in which have been investigated by the approach of bilinear method.
Mainly, by choosing specific parameter constraints in the M-soliton solutions, all cases the periodic and cross-kink solutions can
be captured from the 1-, 2- and 3-soliton. The obtained solutions are extended with numerical simulation to analyze graphically,
which results into 1-, 2- and 3-soliton solutions and also periodic and cross-kink solutions profiles. That will be extensively used
to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics and