Abstract In this work, the (4+1)-dimensional Fokas equation, which is an important physics model, is under investigation. Based on the obtained soliton solutions, the new rational solutions are successfully constructed. Moreover, based on its bilinear formalism, a concise method is employed to explicitly construct its rogue-wave solution and interaction solution with an ansätz function. Finally, the main characteristics of these solutions are graphically discussed. Our results can be helpful for explaining some related nonlinear phenomena.

中文翻译：

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(4+1)维非线性偏微分方程中丰富块的特征和相互作用解

摘要 在这项工作中，(4+1) 维Fokas 方程是一个重要的物理模型，正在研究中。基于获得的孤子解，成功构建了新的有理解。此外，基于其双线性形式，采用简洁的方法显式构建其流氓波解决方案和具有 ansätz 函数的交互解决方案。最后，以图形方式讨论了这些解决方案的主要特征。我们的结果有助于解释一些相关的非线性现象。