Ubiquitous rogue waves

This talk is devoted to rogue waves. This novel scientific term was born in nautical mythology, entered the science of ocean waves [1-3] and gradually moved into other fields: optics [4-7], matter waves [8], superfluids [9], capillary waves [10], plasmas and many others [11]. There is a multiplicity of mathematical descriptions of rogue waves. Variety of ideas how the waves gain higher amplitudes than expected is also large. Linear theories exist on the same right as nonlinear ones. The most common approach is based on the nonlinear Schrdinger equation [1]. The basic phenomenon related to this description is Benjamin-Fair!or Bespalov-Talanov instability or more generally speaking modulation instability. Peregrine first noticed [12] that such instability can be responsible for a quick increase in the wave amplitude in the ocean. A set of special rational solutions localized both in space and time is one of the models of rogue waves that is well developed by now [13,14]. In optical fibers, the major phenomenon that results in high amplitude pulses is modulation instability and inelastic interaction of solitons [5-7]. The latter is caused by third order dispersion and Raman effect and leads to a multiple amplification of stronger solitons [11,15]. � 2011 IEEE.