It is well known that the celebrated Kadomtsev-Petviashvili (KP) equation has many important applications. The aim of this article is to use fractional KP equation to not only simulate shallow ocean waves but also construct novel spatial structures. Firstly, the definitions of the conformable fractional partial derivatives and integrals together with a physical interpretation are introduced and then a fractional integrable KP equation consisting of fractional KPI and KPII equations is derived. Secondly, a formula for the fractional -soliton solutions of the derived fractional KP equation is obtained and fractional line one-solitons with bend, wavelet peaks, and peakon are constructed. Thirdly, fractional X-, Y- and 3-in-2-out-type interactions in the fractional line two- and three-soliton solutions of the fractional KPII equation are simulated for shallow ocean waves. Besides, a falling and spreading process of a columnar structure in the fractional line two-soliton solution is also simulated. Finally, a fractional rational solution of the fractional KP equation is obtained including the lump solution as a special case. With the development of time, the nonlinear dynamic evolution of the fractional lump solution of the fractional KPI equation can change from ring and conical structures to lump structure.

中文翻译：

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基于分数KP方程的浅海浪线孤子相互作用和具有Peakon，环形，圆锥形，柱状和块状结构的新颖解

众所周知，著名的Kadomtsev-Petviashvili（KP）方程具有许多重要的应用。本文的目的是使用分数KP方程不仅模拟浅海浪，而且构造新颖的空间结构。首先介绍了相容分数阶偏导数和积分的定义以及物理解释，然后推导了由分数KPI和KPII方程组成的分数可积KP方程。其次，分数的公式-得到了导出的分数KP方程的孤子解，并构造了具有弯曲，小波峰和峰值的分数线单孤子。第三，针对浅海浪，模拟了分数KPII方程的分数线二孤子解和三孤子解中的分数X，Y和3合2型相互作用。此外，还模拟了分形两孤子解中柱状结构的塌落扩展过程。最终，获得了分数KP方程的分数有理解，其中包括作为特殊情况的整解。随着时间的发展，分数KPI方程的分数集解的非线性动力学演化可能会从环状结构和圆锥结构变为块状结构。