Dirac monopole potentials with high charges underlying nonlinear waves

TL;DR

This paper explores topological vector potentials in nonlinear waves using Dirac monopole theory, revealing higher charge virtual monopoles linked to poles of the density function, contrasting previous findings.

Contribution

It introduces the concept of higher charge virtual monopoles in nonlinear waves, connecting poles of density functions to quantized magnetic charges.

Findings

Poles of density functions correspond to virtual monopoles with charges ±3/2 and ±5/2.

Simple zeros of density functions yield monopole charges of ±1/2.

Demonstrates Dirac monopole potentials in rogue waves and bright solitons.

Abstract

We investigate topological vector potentials underlying the phases of nonlinear waves by performing Dirac's magnetic monopole theory in an extended complex plane, taking into account self-steepening effects while ignoring the usual cubic nonlinearities. We uncover that the simple poles and third-order poles of the density function constitute virtual monopole fields with higher charges $\pm3/2$ and $\pm5/2$, respectively. These results are in sharp contrast to the previous findings, where the simple zeros of the density function yield charges $\pm1/2$. We choose scalar and vector rogue waves as well as bright solitons to demonstrate the Dirac monopole potentials. These results confirm a series of quantized magnetic charges for virtual monopoles underlying nonlinear waves, and reveal new relations between poles of density functions and topological charges.