Mathematical modeling of rogue waves: A survey of recent and emerging mathematical methods and solutions

Abstract

Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly active field of research, which has evolved over the last few decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for the prediction of rogue ocean waves and for signal processing in quantum units. In this survey, a comprehensive perspective of the most recent developments of methods for representing rogue waves is given, along with discussion of the devised forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and other models are discussed and their properties highlighted. This survey shows that the most recent advancement in modeling rogue waves give models that can be used to establish methods for the prediction of rogue waves in open seas, which is important for the safety and activity of marine vessels and installations. The study further puts emphasis on the difference between the methods and how the resulting models form the basis for representing rogue waves in various forms, solitary or with a wave background. This review has also a pedagogic component directed towards students and interested non-experts and forms a complete survey of the most conventional and emerging methods published until recently.