标题： 高阶有理孤子和类似 rogue 波解的(2+1)维非线性流体力学方程 显示英文标题

标题： Higher-order rational solitons and rogue-like wave solutions of the (2+1)-dimensional nonlinear fluid mechanics equations

摘要： 报告了用于(2+1)维Kadomtsev-Petviashvili(KP)方程及其扩展的新型广义摄动(n, M)-重Darboux变换(DTs)，这是通过Darboux矩阵的泰勒展开得到的。 广义摄动(1, N-1)-重DTs被用来以行列式形式找到它们的高阶有理孤子和 rogue wave 解。 详细讨论了这些 rogue waves 在不同参数和时间下的动力学行为，展示了有趣的 RW 和孤子结构，包括三角形、五边形、七边形等轮廓。 此外，我们发现了一个新现象，即参数(a)可以在(x, t)-空间中，当y=常数时，将KP方程的高阶 rogue waves (a>0或a<0) 控制到高阶有理孤子(a = 0)。 这些结果可能预测流体力学和其他物理相关系统中的相应动力学现象。 显示英文摘要

摘要： The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1, N-1)-fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a>0 or a<0) into higher-order rational solitons (a = 0) in (x, t)-space with y=const. These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.