In the present article, our main aim is to construct abundant exact solutions for the \((2+1)\)-dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony (KP-BBM) equation by using two powerful techniques, the Lie symmetry method and the generalised exponential rational function (GERF) method with the help of symbolic computations via Mathematica. Firstly, we have derived infinitesimals, geometric vector fields, commutation relations and optimal system. Therefore, the KP-BBM equation is reduced into several nonlinear ODEs under two stages of symmetry reductions. Furthermore, abundant solutions are obtained in different shapes of single solitons, solitary wave solutions, quasiperiodic wave solitons, elastic multisolitons, dark solitons and bright solitons, which are more relevant, meaningful and useful to describe physical phenomena due to the existence of free parameters and constants. All these generated exact soliton solutions are new and completely different from the previous findings. Moreover, the dynamical behaviour of the obtained exact closed-form solutions is analysed graphically by their 3D, 2D-wave profiles and the corresponding density plots by using the mathematical software, which will be comprehensively used to explain complex physical phenomena in the fields of nonlinear physics, plasma physics, optical physics, mathematical physics, nonlinear dynamics, etc.

在本文中，我们的主要目的是为\（（2 + 1）\）构建丰富的精确解通过使用两种强大的技术，Lie对称方法和广义指数有理函数（GERF）方法，借助借助Mathematica的符号计算，对Kadomtsev–Petviashvili-Benjamin–Bona–Mahony（KP-BBM）方程进行了三维求解。首先，我们导出了无穷小，几何矢量场，换向关系和最优系统。因此，在对称性降低的两个阶段下，KP-BBM方程被还原为几个非线性ODE。此外，以单孤子，孤波解决方案，准周期波孤子，弹性多孤子，暗孤子和亮孤子的不同形状获得了丰富的解，由于存在自由参数和实子，它们对于描述物理现象更相关，有意义和有用。常数。所有这些生成的精确孤子解都是新的，并且与以前的发现完全不同。此外，使用数学软件，通过获得的精确封闭形式解的3D，2D波轮廓和相应的密度图，以图形方式分析它们的动力学行为，这将被广泛用于解释非线性领域中的复杂物理现象。物理学，等离子物理学，光学物理学，数学物理学，非线性动力学等。