Kadomtsev-Petviashvili（KP）方程族是数学物理领域研究的热点之一，它有重要的零约束系统。在拟微分算子的零约束条件下，KP方程族可退回到KdV方程族，也可退回到Boussinesq方程族。在本项目中，我们将借助KP方程族的Lax算子L以及算子L的零约束条件，结合Nambu 3-括号的性质，构造基于Lax 3-对的完全可积的新的KP约束系统，推出广义KdV方程族和广义Boussinesq方程族，并分析这些方程的可积性和对称性，求出它们的精确解，进而研究这些方程在数学物理中的应用。

Kadomtsev-Petviashvili (KP) hierarchy is one of the hot topics in the field of mathematical physics, which has an important zero-constraint system. Under the zero-constraint conditions of the pseudo-differential operator, KP hierarchy can be returned to KdV hierarchy and also back to Boussinesq hierarchy. In this project, using the Lax operator L and the zero-constraint conditions of KP hierarchy, and the properties of Nambu 3-bracket, we will try to construct a new completely integrable KP constrained system based on the Lax triple. Furthermore, we will derive the generalized KdV hierarchy and the generalized Boussinesq hierarchy. We will also analyze their integrability and symmetries, and study their exact solutions. Finally, we will try to find the applications of the equations in mathematical physics.