This study aims to investigate the (2 + 1)-dimensional Kadomtsev-Petviashvili equation via the three-waves method through the Hirota bilinear form and the Kudryashov’s method. Multi-waves solutions and exponential function solutions are successfully extracted. To share more light to the physical features of the reported results, the interaction phenomenon of these obtained solutions are demonstrated by some 3-dimensional and contour plots. All the reported results have tested to satisfy the original nonlinear partial differential equation.

中文翻译：

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通过两种有效的分析技术构造Kadomtsev-Petviashvili方程的多波复数解

本研究旨在通过Hirota双线性形式和Kudryashov方法，通过三波方法研究（2 +1）维Kadomtsev-Petviashvili方程。成功地提取了多波解和指数函数解。为了与报告结果的物理特征共享更多的光，这些获得的解决方案的相互作用现象通过一些三维和等高线图得到了证明。所有报告的结果都经过测试，可以满足原始的非线性偏微分方程。