This study investigates the (3+1)-dimensional soliton equation via the Hirota bilinear approach and symbolic computations. We successfully construct some new lump, lump-kink, breather wave, lump periodic, and some other new interaction solutions. All the reported solutions are verified by inserting them into the original equation with the help of the Wolfram Mathematica package. The solution’s visual characteristics are graphically represented in order to shed more light on the results obtained. The findings obtained are useful in understanding the basic nonlinear fluid dynamic scenarios as well as the dynamics of computational physics and engineering sciences in the related nonlinear higher dimensional wave fields.

中文翻译：

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（3 + 1）维孤子方程的新块，块扭，呼吸波和其他相互作用解

本研究通过Hirota双线性方法和符号计算研究了（3 + 1）维孤子方程。我们成功地构造了一些新的块，块扭，呼吸波，周期性的块以及其他一些新的交互解决方案。在Wolfram Mathematica软件包的帮助下，将所有报告的解决方案插入原始方程式中，从而对所有报告的解决方案进行了验证。以图形方式显示解决方案的视觉特征，以便更多地了解获得的结果。获得的发现有助于理解基本的非线性流体动力学场景以及相关的非线性高维波场中的计算物理和工程科学的动力学。