The prime objective of this paper is to obtain the exact soliton solutions by applying the two mathematical techniques, namely, Lie symmetry analysis and generalized exponential rational function (GERF) method to the (2+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili (g-CHKP) equation. First, we obtain Lie infinitesimals, possible vector fields, and commutative product of vectors for the g-CHKP equation. By the means of symmetry reductions, the g-CHKP equation reduced to various nonlinear ODEs. Subsequently, we implement the GERF method to the reduced ODEs with the help of computerized symbolic computation in Mathematica. Some abundant exact soliton solutions are obtained in the shapes of different dynamical structures of multiple-solitons like one-soliton, two-soliton, three-soliton, four-soliton, bell-shaped solitons, lump-type soliton, kink-type soliton, periodic solitary wave solutions, trigonometric function, hyperbolic trigonometric function, exponential function, and rational function solutions. Consequently, the dynamical structures of attained exact analytical solutions are discussed through 3D-plots via numerical simulation. A comparison with other results is also presented.

中文翻译：

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获得广义 Camassa–Holm–Kadomtsev–Petviashvili 方程精确孤子解的李对称分析

本文的主要目标是通过将李对称分析和广义指数有理函数 (GERF) 方法这两种数学技术应用于 (2+1) 维广义 Camassa–Holm–Kadomtsev– 来获得精确的孤子解。 Petviashvili (g-CHKP) 方程。首先，我们获得了 g-CHKP 方程的李无穷小、可能的向量场和向量的交换积。通过对称简化，g-CHKP 方程简化为各种非线性 ODE。随后，我们在计算机符号计算的帮助下对简化的 ODE 实施 GERF 方法数学. 在多孤子的不同动力学结构形状下，得到了丰富的精确孤子解，如一孤子、二孤子、三孤子、四孤子、钟形孤子、块型孤子、扭结型孤子、周期孤立波解、三角函数、双曲三角函数、指数函数和有理函数解。因此，通过数值模拟通过 3D 图讨论获得的精确解析解的动力学结构。还提供了与其他结果的比较。