Experimental observation of periodic Korteweg-de Vries solitons along a torus of fluid

¹ Université Paris Cité, CNRS, MSC, UMR 7057 - F-75013 Paris, France
² Université Paris-Saclay, CNRS, LISN, UMR 9015 - F-91405 Orsay, France

^(a) filip.novkoski@u-paris.fr
^(b) chi-tuong.pham@upsaclay.fr
^(c) eric.falcon@u-paris.fr (corresponding author)

Received: 14 June 2022
Accepted: 16 August 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 the 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.