Doubly localized two-dimensional rogue waves for the Davey–Stewartson I equation in the background of dark solitons or a constant, are investigated by employing the Kadomtsev–Petviashvili hierarchy reduction method in conjunction with the Hirota’s bilinear technique. These two-dimensional rogue waves, described by semi-rational type solutions, illustrate the resonant collisions between lumps or line rogue waves and dark solitons. Due to the resonant collisions, the line rogue waves and lumps in these semi-rational solutions become doubly localized in two-dimensional space and in time. Thus, they are called line segment rogue waves or lump-typed rogue waves. These waves arise from the background of dark solitons, then exist in the background of dark solitons for a very short period of time, and finally completely decay back to the background of dark solitons. In particular circumstances which are characterized by special parametric conditions, the dark solitons in the long wave component of the DSI equation can degenerate into the constant background. In this case, the rogue waves appear and disappear in a constant background.

通过采用 Kadomtsev-Petviashvili 层次减少方法结合 Hirota 双线性技术，研究了在暗孤子或常数背景下 Davey-Stewartson I 方程的双局部二维流氓波。这些由半有理类型解描述的二维无规律波说明了团块或线无规律波与暗孤子之间的共振碰撞。由于共振碰撞，这些半有理解中的线流氓波和团块在二维空间和时间上双重定位。因此，它们被称为线段流氓波或块状流氓波。这些波从暗孤子的背景中产生，然后在暗孤子的背景中存在很短的时间，最后完全衰变回到暗孤子的背景。在具有特殊参数条件的特殊情况下，DSI方程长波分量中的暗孤子可以退化为恒定背景。在这种情况下，流氓波在恒定背景中出现和消失。