Transverse Instability of Rogue Waves

Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability

Rogue waves lead to the instability in GaN semiconductors

A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains,...

Modulational instability and rogue waves in shallow water models

It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, su...

Real world ocean rogue waves explained without the modulational instability

Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually t...

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...