A Predictable Rogue Wave and Generating Mechanisms

Abstract: Due to the widely applications in almost all branches of science, high dimensional KP equation is selected as universal model to describe rogue wave phenomenon. A lump is an algebraically localized wave decayed in all space directions and exists in all time. Starting from a special lump containing seven arbitrary independent parameters and four constraint conditions with all the physical properties shown, an invisible lump is found with the combination of lump part and exponential part. Because of the domination of the exponential part, the lump will be invisible in some special area, or the lump is cutoff by the induced visible soliton. While the lump part remains invariant, lump will keep its positions, path and amplitude before it is invisible. Furthermore, as a rogue wave/instanton is a localized wave decayed in all space and time directions, a rogue wave / instanton can also be produced by cutting a lump between two visible solitons. The special dispersive for the visible soliton(s) shows the soliton(s) are completely determined by the lump or the visible soliton(s) are induced by the lumps. Because the induced soliton(s) is visible, it is possible to give a prediction of the positions, the wave height and even the path for such kind of rogue waves.