In recent years, searching for analytic solutions to nonlinear evolution equations has become a popular topic. In this paper, a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation is proposed. With the help of symbolic calculation, the multiple-soliton and lump-kink solutions of the equation are obtained in two different ways. Those analytic solutions are presented, and their dynamic properties are discussed through graphical presentation. The final result is helpful for studying the interaction between solitons in nonlinear mathematical physics.

中文翻译：

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广义（3 + 1）维Kadomtsev-Petviashvili方程的多孤子解和扭结解

近年来，寻找非线性发展方程的解析解已成为热门话题。本文提出了广义的（3 + 1）维Kadomtsev-Petviashvili方程。借助于符号计算，可以通过两种不同的方式获得方程的多孤子和整体扭结解。提出了这些解析解决方案，并通过图形表示形式讨论了它们的动态特性。最终结果有助于研究非线性数学物理中孤子之间的相互作用。