Math explains water disasters
The use of Peregrine's theory to explain
disasters is made possible with fibre-optics.
Image: Henry Brett, Flickr CC-licensed.

State-of-the-art optical fibre technology and a 27 year old mathematical theory have been used to demonstrate how extreme events occur - from financial disasters to rogue waves and stampedes - according to researchers from The Australian National University.

An international team of researchers, including Professor Nail Akhmediev from the ANU Research School of Physical Sciences and Engineering, have observed the well-known mathematical prediction, ‘Peregrine’s Soliton’, for the first time. Named after British scientist Howell Peregrine, this theoretical result describes how giant, nonlinear water waves can both grow and decline extremely quickly.

The observation was made not in water, however, but in intense light pulses in optical fibres. The outcome, which was a near-perfect representation of Peregrine’s prediction, could shed new light on the frequency of seemingly extreme events in both the natural and man-made world. The researchers’ paper on the subject is published in Nature Physics.

“Having observed this effect in optical fibres it can serve as a prototype for a wide range of extreme events in nature and social life such as financial disasters, ocean rogue waves, stampedes, climate catastrophes and a variety of other cataclysms,” said Professor Akhmediev.

“From this, we’ve been able to build a class of solutions that can describe more detailed structure of events that can be called ‘extreme’ which shows that extreme events are present in many situations. Their mathematical description is an important step in understanding, prevention and, to some degree, even use.”

The breakthrough was possible because of decades of development in fibre-optics and ultrafast optics instrumentation – something that wasn’t possible when Peregrine came up with his solution in 1983.

“Using light to perform these experiments has many advantages, not least of which is there is no physical danger to the experimenters,” said Professor Akhmediev. “From this, we’ve been able to show that a mathematically perfect Peregrine solution may never actually be observable in practice, but that its intense localisation appears even under non-ideal conditions.

“This is an especially important result for understanding how high-intensity rogue waves may form in the very noisy and imperfect environment of the open ocean”

A copy of the paper is available from the ANU Media office.

Editor's Note: Original news release can be found here.