Dirac Monopoles in Rogue Waves

TL;DR

This paper reveals that rogue waves inherently contain Dirac monopoles, explaining their mysterious behavior and linking their amplification and phase properties to these monopoles, with significant implications for nonlinear wave physics.

Contribution

It is the first demonstration that rogue waves contain Dirac monopoles, providing a novel physical explanation for their properties and behaviors.

Findings

Rogue waves contain Dirac monopoles with quantized flux.

The appearance and disappearance of rogue waves are explained by monopole collision mechanisms.

The amplification and phase steps of rogue waves are related to the number of contained monopoles.

Abstract

We for the first time demonstrate that the widely existed nonlinear waves such as rogue waves, contain Dirac monopoles. We find that the density zeros of these nonlinear waves on an extended complex plane can constitute the Dirac virtual magnetic monopole fields with a quantized flux of elementary $\pi$. We then can explain the exotic property of ``appearing from nowhere and disappearing without a trace" of rogue waves by means of a Dirac monopole collision mechanism. The maximum amplification ratio and multiple phase steps of high-order rogue waves are found to be closely related to the number of their contained monopoles. Important implications of the intrinsic virtual magnetic monopole fields are discussed.