Doubly localized two-dimensional rogue waves in the Davey-Stewartson I equation. (English) Zbl 1472.35089
Summary: 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.
MSC:
| 35C08 | Soliton solutions |
| 35C11 | Polynomial solutions to PDEs |
| 35F10 | Initial value problems for linear first-order PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
Keywords:
semi-rational solution; Kadomtsev-Petviashvili (KP) hierarchy reduction method; Hirota’s bilinear technique; line rogue waves; dark solitonsSoftware:
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