BUFFALO, N.Y., Oct. 4 (UPI) -- Solitary waves or solitons, sometimes called lone wolf waves, are just what they sound like. Unlike normal waves, these nonlinear waves persist without dissipating -- maintaining their shape, speed and energy even after colliding with other waves.
A new mathematical solution, developed by scientists at the University of Buffalo, predicts the phenomenon using much simpler mathematics than previous efforts.
In the 1960s, physicists Norman Zabusky and Martin Kruskal developed a solution to the Korteweg-de Vries equation, an equation that describes the action of solitons. Their solution approximated the waves' formation, but solving the mathematical equation required sophisticated computer-based calculations, limiting scientists' ability to study the finer details of the enigmatic waves.
In a new study published in the journal Physical Review Letters, Buffalo researchers detailed a simpler solution to the Korteweg-de Vries equation.
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"Zabusky and Kruskal's famous work from the 1960s gave rise to the field of soliton theory," Gino Biondini, a professor of mathematics at Buffalo, explained in a news release. "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."
Unlike the previous solution, which failed to predict the types of waves scientists witnessed in nature, the latest solution allows scientists to predict the appearance of solitons given a set of environmental parameters.
Researchers in Europe and Japan used the work of Biondini and his colleague Guo Deng, a PhD candidate in physics, to produce lone wolf waves in a model wave generator. The miniature waves matched the predictions of Biondini and Deng.
The model also revealed a related phenomenon called recurrence, whereby a smooth wave splits into several solitons before recombining once more into a single smooth wave.
"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," explained Miguel Onorato, a physicist at the University of Turin.
