In fluid mechanics, the higher-dimensional and higher-order equations are constructed to describe the propagations of nonlinear waves. In this paper, we investigate the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics. The $N$th-order Pfaffian solutions are constructed and proved via the modified Pfaffian technique. The higher-order soliton, first- and second-order breather solutions are constructed based on the $N$th-order Pfaffian solutions. We graphically demonstrate that the amplitudes and velocities of the solitons are affected by some variable coefficients. Hybrid solutions composed of breathers, lumps and solitons are illustrated graphically. It can be found that when certain parameters are chosen, the breathers, lumps and solitons included in the hybrid solutions possess the same properties as those of the breather and lump solutions.

在流体力学中，构造高维和高阶方程来描述非线性波的传播。在本文中，我们研究了流体力学中的 (2+1) 维变系数 Caudrey-Dodd-Gibbon-Kotera-Sawada 方程。这$N$通过改进的 Pfaffian 技术构建和证明了三阶 Pfaffian 解。高阶孤子、一阶和二阶呼吸器解是基于$N$三阶普法夫解。我们以图形方式证明了孤子的振幅和速度受一些可变系数的影响。由呼吸器、团块和孤子组成的混合解决方案以图形方式说明。It can be found that when certain parameters are chosen, the breathers, lumps and solitons included in the hybrid solutions possess the same properties as those of the breather and lump solutions.