Recent work on second sound acoustic turbulence in superfliud '̂ He is reviewed. Observations of forward and inverse energy cascades are described. The onset of the inverse cascade occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is...

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time sc...

We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter-the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkab...

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized...

Recent work by our research group has shown that wave damping can have a surprisingly strong effect on the evolution of waves in deep water, even when the damping is weak. Whether damping is or is not included in a theoretical model can change the outcome in terms of both stability of wave patterns and frequency downshifting. It is conceivable that it might affect the early development of rogue...

We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.

We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed the formation of solitary waves that will appear during the modulation instability process at those preferred intervals. Afterwards, optical-event horizon effe...

A resonance between long and short waves will occur if the phase velocity of the long wave matches the group velocity of the short wave. In this paper, a system with two distinct packets of short waves in resonance with a common long wave is studied. Breather solutions are calculated by the Hirota bilinear method, and rogue wave modes (unexpectedly large displacements from an otherwise calm bac...