Reference: Europhysics
Letters (EPL) 139, 53003 (2022) 
Abstract:
We report on the experimental observation of solitons
propagating along a torus of fluid. We show that such a periodic
system leads to significant differences compared to the
classical plane geometry. In particular, we highlight the
observation of subsonic elevation solitons, and a nonlinear
dependence of the soliton velocity on its amplitude. The soliton
profile, velocity, collision, and dissipation are characterized
using high resolution space-time measurements. By imposing
periodic boundary conditions onto Korteweg-de Vries (KdV)
equation, we recover these observations. A nonlinear spectral
analysis of solitons (periodic inverse scattering transform) is
also implemented and experimentally validated in this periodic
geometry. Our work thus reveals the importance of periodicity
for studying solitons and could be applied to other fields
involving periodic systems governed by a KdV equation.