This letter investigates the temporally localized lumps on a background of two-dimensional (2D) homoclinic orbits in the Fokas system. These special lumps are localized in time as well as in 2D space and have completely different dynamical behaviours compared with usual lumps, and they are called “rogue lumps”. It is shown that these rogue lumps first arise from homoclinic orbits, and then remain propagating with their identities unaltered for a very short period of time after the former homoclinic orbits are disappearing, and finally decay into other new homoclinic orbits. These rogue lumps appear and disappear jointly with 2D homoclinic orbits, and are important in understanding the extreme waves phenomena in physical settings.

这封信调查了 Fokas 系统中二维 (2D) 同宿轨道背景上的时间局部团块。这些特殊的块在时间和二维空间中都是局部的，与通常的块相比具有完全不同的动力学行为，它们被称为“流氓块”。结果表明，这些流氓团块首先来自同宿轨道，然后在之前的同宿轨道消失后，在很短的时间内保持原样不变地传播，最后衰变为其他新的同宿轨道。这些流氓团块与 2D 同宿轨道一起出现和消失，对于理解物理环境中的极端波现象很重要。