Rogue wave is a kind of wave that possesses concentrated energy, strong nonlinear and enormous devastating. When it interacts with the deep-sea structures, the structure will suffer a serious threat, and it may even cause significant harm to the offshore staff and property. Studies on the mechanism of rogue wave are of great significance to the platform design and security. It is also one of the hot issues on the waves of hydrodynamic studies. Some breather-type solutions of NLS equation have been considered as prototypes of rogue waves in ocean. They can appear from smooth initial condition only with a certain disturb given by the exact solution of NLS. In this paper, we have numerically studied rogue waves based on fourth order nonlinear Schrödinger equation. We show that the peaks of the largest amplitude of the resulting waves can be described in terms of the Peregrine breather-type solution as the solution of NLS equation.
Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces
