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

Area of Science:

• Nonlinear physics
• Wave phenomena
• Extreme event dynamics

Background:

• Rogue waves (RWs) are exceptionally high, transient waves, first scientifically measured in 1995.
• RWs have been observed in diverse systems, including optics, fluids, plasmas, and financial markets.
• The study of RWs spans nearly a century of anecdotal evidence and decades of scientific investigation.

Purpose of the Study:

• To compile recent advancements in rogue wave research.
• To present a collection of theoretical, computational, and experimental studies on rogue waves.
• To highlight the interdisciplinary nature and broad applicability of rogue wave phenomena.

Main Methods:

• Analysis of classical evolution systems, particularly nonlinear Schrödinger equations.
• Theoretical modeling and numerical simulations of wave dynamics.
• Experimental investigations across various physical domains.

Main Results:

• Comprehensive review of current progress in rogue wave research.
• Exploration of applications in lasers, layered fluids, ferromagnetic materials, and geophysical flows.
• Documentation of advances utilizing machine learning and neural networks for rogue wave analysis.

Conclusions:

• Rogue wave research has progressed significantly since the Draupner wave measurement.
• Interdisciplinary approaches and advanced computational methods are crucial for understanding RWs.
• Future research directions include leveraging AI for further insights into these extreme events.