Localized Structures in Dissipative Nonlinear Systems - Abstract
Akhmediev, Nail
One of the main features of a rogue wave is its äppearance from nowhere". Indeed, in most cases they arrive completely unexpected. Another basic feature of a rogue wave is that it is characterised by much higher amplitude than the average waves around. By now scientists agreed [1] that the wave with an amplitude that exceeds more than twice the significant wave hight around can be called a rogue wave. While it is expected that linear theories predict probability of events with such amplitudes that are beyond being observable, rogue waves in practice happen much more often causing trouble for those who encounter them. Namely, statistics of extreme events are far from being gaussian. Probability of high amplitude events measured experimentally is much higher than predicted by a simple gaussian distribution. Rogue waves exist in a wide range of physical systems including open ocean, optics, space plasma, economy and finances, superfluids, capillary waves etc. Generally speaking, rogue waves are those localised both in space and time. As such, they can be described by unique solutions of nonlinear wave equations (NWE). Presently, these solutions are neither completely revealed nor understood although they do exist for wide range of NWE. Having mathematical description of a rogue wave is important for practice. Firstly, this knowledge will allow us to calculate the probability for their appearance. In the open ocean, this knowledge is vital for survival of the ships and planning the routes that are less dangerous. Secondly, the theory is important for the knowledge of how to excite a rogue wave. In a laboratory, we are faced with the necessity to excite them. Knowing the precursors that excite the rogue wave may help in forecasting and then the event may not be that much unexpected as it is at present. Finally, an important issue is the possibility to eliminate the rogue wave when it is predicted. Even better, eliminate the mere conditions for their appearance all together. Clearly, the process of elimination or suppression is opposite to excitation. Thus, having the understanding and rigorous mathematical description, we will be able to know what we need to do to remove the rogue waves from the wave field.
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[1] N. Akhmediev and E. Pelinovsky (Eds.) Special Issue of European Physical Journal "Discussion & Debate: Rogue Waves - Towards a unifying concept?", In print. This future book contains around 20 articles by world experts on extreme events in various fields of science.