Rogue waves: Theory, methods, and applications—30 years after the Draupner wave

Abstract

Rogue waves (RWs) are unexpectedly high-amplitude, transient displacements on top of an otherwise tranquil background. While oceanic RWs were known to sailors for nearly a century, the first scientific measurements occurred at an offshore platform in the North Sea in 1995 (the Draupner wave). In 2007, optical RWs were observed in optical fibers. Subsequently, such extreme events were also recorded in capillarity, plasmas, and even in financial markets. Thirty years after the Draupner wave, it is timely to compile a collection of articles representing the current progress in theoretical, computational, and experimental studies. Classical evolution systems, such as families of nonlinear Schrödinger equations, are treated in the articles. Applications to various areas, including lasers, layered fluids, ferromagnetic materials, and geophysical flows, are addressed. Advances based on machine-learning algorithms and neural networks are documented too.