Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulses.

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

Over a decade ago, an analogy was drawn between the generation of large ocean waves and the propagation of light fields in optical fibres. This analogy drove numerous experimental studies in both systems, which we review here. In optics, we focus on results arising from the use of real-time measurement techniques, whereas in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. This Review of the work in hydrodynamics includes results that support both nonlinear and linear interpretations of rogue wave formation in the ocean, and in optics, we also provide an overview of the emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We discuss the insights gained from the analogy between the two systems and its limitations in modelling real-world ocean wave scenarios that include physical effects that go beyond a one-dimensional propagation model.

▪ Abstract This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation of various types of capillary-gravity waves, including two-dimensional solitary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequency downshift phenomenon is provided. Recent significant results are given on “horseshoe” patterns, which are three-dimensional structures observable on the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.