Rogue waves in nonlinear science

Rogue Waves in Higher Order Nonlinear Schrödinger Models

We discuss physical and statistical properties of rogue wave generation in deep water from the perspective of the focusing Nonlinear Schrödinger equation and some of its higher order generalizations. Numerical investigations and analytical arguments based on the inverse spectral theory of the underlying integrable model, perturbation analysis, and statistical methods provide a coherent picture ...

Rogue waves

“It came from nowhere, snapping giant ships in two. No one believed the survivors ... until now” screamed the cover of New Scientist magazine on 30 June 2001, introducing an article entitled “Monsters of the Deep”. The power and danger suggested by the term “rogue” add to the public fascination with extreme ocean waves, but they also present important and challenging scientific problems and pro...

Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability

Rogue waves and rational solutions of the nonlinear Schrödinger equation.

We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue ...

Rogue waves in superfluid helium

Rogue waves have been observed in superfluid helium. The experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the waves are turbulent and there are fluxes of energy towards both high and low frequencies. Rogue waves appear under the non...