A novel type of rogue waves with predictability in nonlinear physics

Abstract: Rogue waves named by oceanographers are ubiquitous in nature and appear in a variety of different contexts such as water waves, liquid Helium, nonlinear optics, microwave cavities, etc. In this letter, we propose a novel type of exact (2+1)-dimensional rogue waves which may be found in many physical fields described by integrable and nonintegrable models. This type of rogue waves are closely related to invisible lumps. Usually, a lump is an algebraically localized wave in space but visible at any time. Whence a lump induces a soliton, the lump will become invisible before or after a fixed time. If a bounded twin soliton is induced by a lump, the lump will become a rogue wave (or instanton) and can only be visible at an instant time. Because of the existence of the induced visible solitons, the rogue wave may be predictable in some senses. For instance, the height, the position and the arrival time of the rogue wave can be predictable. The idea is illustrated by the celebrate (2+1)-dimensional Kadomtsev-Petviashvili equation in its extended form.