In this paper, the soliton solutions and dynamical wave structures for the generalized (3+1)-dimensional shallow water wave (SWW) equation, which is an important physical property in ocean engineering and hydrodynamics, are presented. The generalized exponential rational function (GERF) method is used to investigate the closed-form wave solutions of the generalized SWW equation, which is used to describe the evolutionary dynamics of SWW. We successfully archive a variety of soliton solutions such as exponential solutions, kink wave solutions, non-topological solutions, periodic singular solutions, and topological solutions. These newly established results are also important for understanding the wave-propagation and dynamics of exact solutions of the equation, which is of great significance in physical oceanography and chemical oceanography. Eventually, it is shown that the proposed GERF technique is effective, robust, and straightforward and is also used to solve other types of higher-dimensional nonlinear evolution equations. In our work, we have used Mathematica extensively for such complicated algebraic calculations.

中文翻译：

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广义(3+1)维浅水波动方程的解析孤子解

本文介绍了广义（3+1）维浅水波（SWW）方程的孤子解和动力波结构，该方程是海洋工程和流体动力学中的重要物理性质。广义指数有理函数（GERF）方法用于研究广义SWW方程的封闭形式的波解，用于描述SWW的演化动力学。我们成功归档了指数解、扭结波解、非拓扑解、周期奇异解、拓扑解等多种孤子解。这些新建立的结果对于理解方程精确解的波传播和动力学也很重要，这在物理海洋学和化学海洋学中具有重要意义。最终表明，所提出的 GERF 技术是有效的、稳健的和直接的，并且还用于求解其他类型的高维非线性演化方程。在我们的工作中，我们使用了数学广泛用于如此复杂的代数计算。