广义（3+1）维浅水波方程的Painlevé分析和高阶Rogue波
Painlevé Analysis and Higher-Order Rogue Waves of a Generalized(3+1)-dimensional Shallow Water Wave Equation
摘要：
考虑到探索局域波的重要性，我们研究了一个广义的（3+1）维Hirota-Satsuma-Ito方程描述浅水波的单向传播，并进行Painlevé分析，以了解其可积性的性质。采用Hirota的双线性化和广义多项式函数构造了高阶流氓波解的显式形式。此外，我们详细探讨了它们的动力学，描绘了不同的斑图形成，揭示了其操纵机制中可用的任意常数的潜在优势。特别是，我们证明了存在的单本地化线流氓波和双本地化流氓波与多个（单，三，和六）结构生成三角形和五边形类型的几何图案与可控的方向，可以通过调整参数适当地改变。所提出的分析将是一个重要的包含在上下文中的流氓波在高维系统。
英文摘要：
Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform Painlevé analysis to understand its integrability nature. We construct the explicit form of higher-order rogue wave solutions by adopting Hirota's bilinearization and generalized polynomial functions. Further, we explore their dynamics in detail, depicting different pattern formation that reveal potential advantages with available arbitrary constants in their manipulation mechanism. Particularly, we demonstrate the existence of singly-localized line-rogue waves and doubly-localized rogue waves with multiple (single, triple, and sextuple) structures generating triangular and pentagon type geometrical patterns with controllable orientations that can be altered appropriately by tuning the parameters. The presented analysis will be an essential inclusion in the context of rogue waves in higher-dimensional systems.
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