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 more accurately than ever before.

In the 1960s, physicists Norman Zabusky and Martin Kruskal developed a formula -- the Korteweg-de Vries equation -- to describe the action of solitons. They also came up with a solution to approximate the waves' formation. But solving their 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.

"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 Italy and Japan used the work of Biondini and his colleague Guo Deng, a PhD candidate in physics, to build a water wave generator capable of producing lone wolf waves. The model was able to produce waves matching the predictions of Biondini and Deng.

The model also revealed a related phenomenon called recurrence, whereby a soliton splits into several soliton before recombining once more into a single solitary 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.