Preprint Review Version 3 Preserved in Portico This version is not peer-reviewed

Mathematical Modeling of Rogue Waves, a Survey of Conventional and Emerging Mathematical Methods and Solutions

Version 1 : Received: 16 March 2018 / Approved: 16 March 2018 / Online: 16 March 2018 (13:31:03 CET)
Version 2 : Received: 26 April 2018 / Approved: 27 April 2018 / Online: 27 April 2018 (07:55:12 CEST)
Version 3 : Received: 16 May 2018 / Approved: 17 May 2018 / Online: 17 May 2018 (12:33:32 CEST)
Version 4 : Received: 7 June 2018 / Approved: 9 June 2018 / Online: 9 June 2018 (15:28:58 CEST)

A peer-reviewed article of this Preprint also exists.

Manzetti, S. Mathematical Modeling of Rogue Waves: A Survey of Recent and Emerging Mathematical Methods and Solutions. Axioms 2018, 7, 42. Manzetti, S. Mathematical Modeling of Rogue Waves: A Survey of Recent and Emerging Mathematical Methods and Solutions. Axioms 2018, 7, 42.


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 actual field of research, which has evolved over the last decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for prediction of rogue ocean waves, and for signal processing in quantum units. In this survey, a comprehensive perspective of the most recent developments in methods for representing rogue waves is given, along with discussion of the devised and forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and further to other models are discussed, and their properties highlighted. This survey shows that the most recent advancement in modeling rogue waves give models which can be used to establish methods for prediction of rogue waves at 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 a 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.


rogue; wave; models; KdV; NLSE; non-local; ocean; optics


Physical Sciences, Fluids and Plasmas Physics

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 0
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.