Nav: Home

Study solves 50-year-old puzzle tied to enigmatic, lone wolf waves

October 04, 2016

BUFFALO, N.Y. -- Solitary waves called solitons are one of nature's great curiosities: Unlike other waves, these lone wolf waves keep their energy and shape as they travel, instead of dissipating or dispersing as most other waves do.

In a new paper in Physical Review Letters (PRL), a team of mathematicians, physicists and engineers tackles a famous, 50-year-old problem tied to these enigmatic entities.

The puzzle dates back to 1965, when physicists Norman Zabusky and Martin Kruskal came up with a surprising solution to the Korteweg-de Vries equation, which serves as a mathematical model for describing nonlinear waves in shallow water.

Using a computer, Zabusky and Kruskal generated an approximate solution to the equation that featured eight independent, particle-like waves. Each of these waves retained its form and speed over time and distance -- even after colliding with other such waves. The colleagues coined the term "soliton" to describe these unusual entities, giving birth to modern research in this field.

Kruskal and others then went on to invent a new mathematical method to solve the Korteweg-de Vries equation exactly. However, the calculations needed to obtain concrete answers are complex, typically requiring the use of a computer to complete -- thus limiting scientists' ability to understand phenomena, including Zabusky and Kruskal's 1965 solution, says University at Buffalo mathematician Gino Biondini.

Moreover, to Biondini's knowledge, the original wave pattern that Zabusky and Kruskal described in 1965 has never been fully reproduced in the physical world (though earlier experiments have managed to generate portions of the solution).

The new PRL study, published Sept. 28, addresses both of these problems, says Biondini, a co-author on the paper.

A new approach to an old problem

With Guo Deng, a UB PhD candidate in physics, Biondini developed a mathematical approach that produces an approximate solution to the equation that Zabusky and Kruskal tackled in the 1960s. The new approach enables researchers to make explicit, accurate predictions about how many solitons will emerge in a given setting, as well as what features these waves will have, such as their amplitude and speed.

The method's simplicity means that researchers can use it to gain a better mathematical understanding of soliton formation in these kinds of situations, Biondini says.

"Zabusky and Kruskal's famous work from the 1960s gave rise to the field of soliton theory," says Biondini, a professor of mathematics in the UB College of Arts and Sciences. "But until now, we lacked a simple explanation for what they described. Our method gives you a full description of the solution that they observed, which means we can finally gain a better understanding of what's happening."

Making waves

While Biondini and Deng worked on the theoretical side of the problem, colleagues in Europe and Japan put their math to the test in real-world experiments as part of the same paper.

Led by Italian scientists Miguel Onorato and Stefano Trillo of the University of Turin and the University of Ferrara, respectively, the team ran experiments in a 110-meter-long water tank in Berlin using a computer-assisted wave generator. The wave patterns they produced matched well with Biondini and Deng's predictions, and included the original eight-soliton solution described by Zabusky and Kruskal so many years before (though it should be noted that water waves do begin to lose some energy after traveling over long distances, and are therefore only approximately solitons).

"Previous experiments had produced parts of the famous results from 1965, but, as far as I know, they all had limitations," Onorato says. "We were able to generate the solution more fully, including all eight solitons. We were also able to experimentally generate another feature observed in multi-soliton solutions, namely the strange phenomenon of recurrence, in which a wave pattern transitions from its initial state to a state with several solitons and back again to the original state. This is akin to placing a bunch of children in a room to play, then returning later to find that the room has been returned to its initial, tidy state after a period of messiness."
In addition to UB, the University of Ferrara and the University of Turin, institutions that partnered on the PRL study included the Technical University of Berlin in Germany; Aalto University in Finland; the University of Tokyo in Japan; and the Istituto Nazionale di Fisica Nucleare, Sezione di Torino in Italy.

The study was supported by the Italian Ministry of Education, University and Research; the U.S. National Science Foundation; the Japan Society for the Promotion of Science; and the Burgundy Region.

University at Buffalo

Related Energy Articles:

Quantum vacuum: Less than zero energy
According to quantum physics, energy can be 'borrowed' -- at least for some time.
New discipline proposed: Macro-energy systems -- the science of the energy transition
In a perspective published in Joule on Aug. 14, a group of researchers led by Stanford University propose a new academic discipline, 'macro-energy systems,' as the science of the energy transition.
How much energy storage costs must fall to reach renewable energy's full potential
The cost of energy storage will be critical in determining how much renewable energy can contribute to the decarbonization of electricity.
Energy from seawater
A new battery made from affordable and durable materials generates energy from places where salt and fresh waters mingle.
Shifts to renewable energy can drive up energy poverty, PSU study finds
Efforts to shift away from fossil fuels and replace oil and coal with renewable energy sources can help reduce carbon emissions but do so at the expense of increased inequality, according to a new Portland State University study
Putting that free energy around you to good use with minuscule energy harvesters
Scientists at Tokyo Tech developed a micro-electromechanical energy harvester that allows for more flexibility in design, which is crucial for future IoT applications.
A new way to transfer energy between cells
Researchers have described a new method for the transmission of electrons between proteins that refutes the evidence from experiments until now.
Renewable energy cooperatives, an opportunity for energy transition
Three researchers from the UPV/EHU's Faculty of Engineering -- Bilbao and the University of Valladolid have explored how renewable energy cooperatives have evolved.
MIT Energy Initiative study reports on the future of nuclear energy
In new MIT report, study authors analyze the reasons for the current global stall of nuclear energy capacity and discuss measures that could be taken to arrest and reverse that trend.
Wave energy converters are not geared towards the increase in energy over the last century
Wave energy converters are designed to generate the maximum energy possible in their location and take a typical year in the location as a reference.
More Energy News and Energy Current Events

Top Science Podcasts

We have hand picked the top science podcasts of 2019.
Now Playing: TED Radio Hour

Why do we revere risk-takers, even when their actions terrify us? Why are some better at taking risks than others? This hour, TED speakers explore the alluring, dangerous, and calculated sides of risk. Guests include professional rock climber Alex Honnold, economist Mariana Mazzucato, psychology researcher Kashfia Rahman, structural engineer and bridge designer Ian Firth, and risk intelligence expert Dylan Evans.
Now Playing: Science for the People

#540 Specialize? Or Generalize?
Ever been called a "jack of all trades, master of none"? The world loves to elevate specialists, people who drill deep into a single topic. Those people are great. But there's a place for generalists too, argues David Epstein. Jacks of all trades are often more successful than specialists. And he's got science to back it up. We talk with Epstein about his latest book, "Range: Why Generalists Triumph in a Specialized World".
Now Playing: Radiolab

Dolly Parton's America: Neon Moss
Today on Radiolab, we're bringing you the fourth episode of Jad's special series, Dolly Parton's America. In this episode, Jad goes back up the mountain to visit Dolly's actual Tennessee mountain home, where she tells stories about her first trips out of the holler. Back on the mountaintop, standing under the rain by the Little Pigeon River, the trip triggers memories of Jad's first visit to his father's childhood home, and opens the gateway to dizzying stories of music and migration. Support Radiolab today at