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Light on nonlinearity – Peregrine’s soliton observed at last

20 September 2010 Suomen Akatemia (Academy of Finland)

Despite its central place as a defining object of nonlinear science for over 25 years, the unique characteristics of The Peregrine soliton have never been directly observed in a continuous physical system. Until now.

Howell Peregrine (1938-2007) was a visionary British scientist who made many fundamental contributions to applied mathematics and physics. In 1983, he discovered a particular class of mathematical solution describing giant nonlinear water waves that experience extremely rapid growth followed by just as rapid decay.  His solution – which is now known as the “Peregrine soliton” – is derived from a complex partial differential equation known as the nonlinear Schrödinger equation (NLSE), but it has a remarkably simple mathematical structure that can be computed by any high school student. The Peregrine soliton is of great physical significance because its intense localisation has led it to be proposed as a prototype of the infamous ocean rogue waves responsible for many maritime catastrophes. It also represents a special mathematical limit of a wide class of periodic solutions to the NLSE. 

Somewhat surprisingly, however, despite its central place as a defining object of nonlinear science for over 25 years, the unique characteristics of this very special nonlinear wave have never been directly observed in a continuous physical system. Until now. In a paper in the journal Nature Physics in August, an international research team from France, Ireland, Australia and Finland – Tampere University of Technology – reports the first observation of highly localized waves possessing near-ideal Peregrine soliton characteristics.

Interestingly, the researchers carry out their experiments using light not water, but they are able to rigorously test Peregrine’s prediction by exploiting the mathematical equivalence between the propagation of nonlinear waves on water and the evolution of intense light pulses in optical fibers.  Using light to perform these experiments has many advantages, not the least being that there is no physical danger to the experimenters themselves!  Moreover, by building on decades of advanced development in fiber-optics and ultrafast optics instrumentation, the researchers have been able to explicitly measure the ultrafast temporal properties of the generated soliton wave, and directly and carefully compare their results with Peregrine’s prediction.

The results of the international team represent the first direct measurements of Peregrine soliton localisation in a continuous wave environment in physics. In fact, the authors are careful to remark that a mathematically perfect Peregrine soliton may never actually be observable in practice, but they also show that its intense localisation appears even under non-ideal excitation 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. 

Aside from their intrinsic interest in nonlinear wave theory, the results obtained by the team highlight the important role that experiments from optics can play in clarifying ideas from other domains of science.  In particular, since related dynamics governed by the same NLSE propagation model are also observed in many other systems such as plasmas and Bose Einstein Condensates, the results are expected to stimulate new research directions in many other fields. They also highlight the lasting impact of Howell Peregrine’s work.

Attached files

  • A figure showing a calculated Peregrine soliton upon a distorted background. This illustrates how such extreme wave structures may appear as they emerge suddenly on an irregular surface such as the open ocean. The destructive power of such a steep nonlinear wave on the ocean can be easily imagined.

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