The lump solutions have been shown to be one of the most effective solutions for nonlinear evolution problems. The resilient Hirota bilinear method is used to evaluate the integrable (3+1)-dimensional nonlinear evolution equation in this work. For the problem under scrutiny, we establish novel types of solutions such as breather wave, lump-periodic, and two wave solutions. For easy observation, the physical features of the generated solutions are displayed. The findings of this study can be used to a variety of fields to better understand complex physical processes.

中文翻译：

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块体碰撞现象对（3+1）维非线性演化方程的动力学

集总解已被证明是非线性演化问题最有效的解法之一。在这项工作中，弹性 Hirota 双线性方法用于评估可积 (3+1) 维非线性演化方程。对于正在审查的问题，我们建立了新型解决方案，例如呼吸波、整体周期和两波解决方案。为了便于观察，显示了生成的解决方案的物理特征。这项研究的结果可用于各种领域，以更好地了解复杂的物理过程。