Abstract
The Maccari system is a nonlinear dynamical model for the description of two-dimensional rogue waves occuring in diverse physical settings. For this two-dimensional nonlinear system, the time localized breathers and doubly localized lumps termed as rogue breathers and rogue lumps on a background of dark line solitons are investigated. The rogue breather behaves as a breather appearing and disappearing on a background of two dark line solitons, and is generated from the resonant collision between a breather and two dark line solitons. The limit case of a rogue breather is a rogue lump, which is truly localized in time and in the two-dimensional space. The Nth-order rogue lumps on a background of (N+1) dark line solitons are constructed by employing the Kadomtsev-Petviashvili hierarchy reduction method combined with the Hirota bilinear method. These higher-order lumps arise from a background of dark line solitons and then disappear into the background again after living for a very short period of time. The rogue lumps possess the key features of two-dimensional rogue waves occurring in a plethora of physical settings.
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