Dirac monopole potentials with high charges underlying nonlinear waves

2026/04/29 by Yan-Hong Qin, Jin-Peng Yang, Li-Chen Zhao · 1 voice
Physics and Astronomy · #nlin.PS

paper · pdf

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 ±3/2 and ±5/2, respectively. These results are in sharp contrast to the previous findings, where the simple zeros of the density function yield charges ±1/2. 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.

Citations

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Discussions

• Yan-Hong Qin, Jin-Peng Yang, Li-Chen Zhao: Dirac monopole potentials with high charges underlying nonlinear waves https://arxiv.org/abs/2604.26431 https://arxiv.org/pdf/2604.26431 https://arxiv.org/ht [bsky, 0 points, 0 comments]

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