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Many natural disasters can be related to wave processes, either due to the destructive wave impact, as in the case of tsunamis, storm waves and surges, and oceanic rogue waves, or due to indirect effects, such as wave sediment transport, landslides induced by earthquakes, etc. These phenomena affect millions of people annually and may result in billions of dollars losses. From the scientific point of view, catastrophic wave phenomena are often related to essentially nonlinear dynamics and nontrivial nonlinear effects. Thus, vital practical needs lead to challenges in nonlinear physics and mathematics. The consequent fundamental theoretical problems are important in their own right, and the dynamical understanding develops and may even change in the course of obtaining solutions. The application stage is when the developed theoretical approaches are directed back to the geophysical issue with success in improved understanding, or the contrary, with insufficient effectiveness which motivates further fundamental research.

Advances in nonlinear wave research for hazard warning and mitigation