Based on the prime number [Formula: see text], a generalized (3+1)-dimensional Kadomtsev-Petviashvili (KP)-type equation is proposed, where the bilinear operators are redefined through introducing some prime number. Computerized symbolic computation provides a powerful tool to solve the generalized (3+1)-dimensional KP-type equation, and some exact solutions are obtained including lump-type solution and interaction solution. With numerical simulation, three-dimensional plots, density plots, and two-dimensional curves are given for particular choices of the involved parameters in the solutions to show the evolutionary characteristics.

中文翻译：

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广义(3+1)维Kadomtsev-Petviashvili型方程精确解的符号计算研究

在素数[公式：见正文]的基础上，提出了一个广义的(3+1)维Kadomtsev-Petviashvili (KP)型方程，通过引入一些素数重新定义了双线性算子。计算机符号计算为求解广义(3+1)维KP型方程提供了有力的工具，得到了包括块型解和交互作用解在内的一些精确解。通过数值模拟，给出了求解中所涉及参数的特定选择的三维图、密度图和二维曲线，以显示演化特征。