In this paper, we investigate the exact solutions of a modified generalized multidimensional fractional Kadomtsev–Petviashvili (KP) equation by the bifurcation method. First, the equation is converted into a planar dynamical system through fractional complex wave transformation. The phase portraits of the equation and qualitative analysis are presented under different bifurcation conditions. Then, the bounded and unbounded traveling wave solutions, including periodic, kink, anti-kink, dark-solitary, bright-solitary and breaking wave solutions, are acquired by integrating along different orbits. Finally, numerical simulations of the dynamic behaviors of the solutions obtained are graphically illustrated by choosing appropriate parameters.

在本文中，我们通过分叉法研究了修正的广义多维分数式 Kadomtsev-Petviashvili (KP) 方程的精确解。首先，通过分数复波变换将方程转换为平面动力系统。给出了不同分岔条件下方程的相图和定性分析。然后，通过沿不同轨道积分得到有界和无界行波解，包括周期波解、扭结波解、反扭结波解、暗孤立波解、亮孤立波解和碎波解。最后，通过选择适当的参数，以图形方式说明所获得的解决方案的动态行为的数值模拟。