Envelope solitons and wave structures in the (2+1)-dimensional KP equation

The main purpose of this paper is to investigate the recently introduced (2+1)-dimensional integrable Kadomtsev–Petviashvili equation, and explore numerous exact solutions, including breather wave, periodic wave, two-wave solutions, the kink-cross, [Formula: see text], and [Formula: see text] types solution. Soliton solutions are examined including bright envelope soliton solutions, dark envelope soliton solutions, periodic solutions, and ratio of exponential functions solutions. The graphical representations highlight the various dynamic characteristics of these solutions.