Gauge-Theoretical Method in Solving Zero-Curvature Equations: I. Application to the Static Einstein–Maxwell Equations with Magnetic Charge

Abstract The inverse scattering problem is applied to 2D partial differential equations called soliton equations such as the Korteweg–de Vries equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse scattering problems look different. We show that t...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2025; no. 2
Main Authors Azuma, Takahiro, Koikawa, Takao
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.02.2025
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ISSN2050-3911
2050-3911
DOI10.1093/ptep/ptaf020

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Summary:Abstract The inverse scattering problem is applied to 2D partial differential equations called soliton equations such as the Korteweg–de Vries equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse scattering problems look different. We show that they can be understood in a unified way. As an application to the Einstein equation, we find solutions of the Einstein–Maxwell equations with a magnetic charge.
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptaf020