Rogue waves: Analytical predictions

Rogue waves observed in the ocean and elsewhere are often modelled by certain solutions of the nonlinear Schrodinger equation, describing the modulational instability of a plane wave and the subsequent development of multi-phase nonlinear wavetrains. In this paper, we describe how integrability and application of the inverse scattering transform can be used to construct a class of explicit asymptotic solutions which describe this process. We discuss the universal mechanism of the onset of multi-phase nonlinear wave (rogue waves) through the sequence of succesive multi-breather wavetrains. Some applications to ocean waves and laboratory experiments are presented.