Solitons Take Their Lumps in Two Dimensions
Solitons are solitary waves that travel like particles without changing shape. They have primarily been observed in settings where the underlying physics is 1D, such as along narrow water channels or inside thin optical fibers, but they can occur in higher dimensions as well. Davide Pierangeli from Sapienza University of Rome and his colleagues have used a structured light beam to become the first to produce a lump soliton, a mathematically exact soliton in two dimensions [1].
Solitary waves are known to occur in higher dimensions, with the most familiar example being “rogue waves” in the ocean. But these waves are not “integrable” solitons, Pierangeli explains. By that he means they are not exact solutions to a nonlinear model describing the wave behavior. “Genuine solitons have an elegant mathematical formulation that makes their behavior deterministic,” he says. Thanks to this property, integrable solitons maintain their shapes and can bounce elastically off each other when they collide.
Over 40 years ago, theorists predicted that integrable solitons could form on a 2D fluid surface, but generating these lump solitons required an impractically large surface tension [2]. Pierangeli and his colleagues circumvented this problem by reproducing the lump-soliton model optically. A spatial light modulator imprinted a soliton-shaped peak on a laser beam’s 2D cross section. After the light traversed a nonlinear crystal, the researchers found the soliton shape intact, as expected. They also observed elastic collisions between two solitons sent along controlled trajectories across the beam’s profile.
The results could help explain nonlinear fluid phenomena, such as phenomena observed in microgravity experiments. In the longer term, this soliton demonstration might influence efforts in developing energy-efficient computing devices (see Viewpoint: Riding Waves in Neuromorphic Computing).
–Michael Schirber
Michael Schirber is the Deputy Editor of Physics Magazine.
References
- L. Dieli et al., “Observation of lump solitons,” Phys. Rev. Lett. 136, 053804 (2026).
- J. Satsuma and M. J. Ablowitz, “Two-dimensional lumps in nonlinear dispersive systems,” J. Math. Phys. 20, 1496 (1979).