Observation of Kuznetsov-Ma soliton dynamics in optical fibre

TLDR

The nonlinear Schrödinger equation, a key model across physics, admits few analytic solutions, including the Kuznetsov‑Ma soliton, yet no quantitative experiments had confirmed this localized soliton on a finite background. The study reports novel optical‑fiber experiments that confirm the Kuznetsov‑Ma soliton theory, completing a series that observed the full family of soliton‑on‑background solutions to the NLSE. The experiments confirm the Kuznetsov‑Ma soliton theory and demonstrate that its dynamics are more universal than originally thought, providing an analytic description of Fermi‑Pasta‑Ulam recurrence in NLSE propagation.

Abstract

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.