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Inverse scattering, differential geometry Einstein-Maxwell solitons and one Soliton Bäcklund transformations

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Solutions of Einstein's Equations: Techniques and Results

Part of the book series: Lecture Notes in Physics ((LNP,volume 205))

Abstract

A survey of the method inverse scattering transform is given and a differential geometric interpretation of the inverse scattering equations is presented. Einstein-Maxwell field equations for space-times admitting nonnull commuting two Killing vector fields are integrated by giving the 2N-soliton construction. One soliton constructions of the gravitational field and of the self-dual Yang-Mills field equations are shown to be equivalent to the recently found Bäcklund transformations.

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Authors and Affiliations

  1. Department of Applied Mathematics, Marmara Research Institute, P.O. Box 21, Gebze, Kocaeli, Turkey

    Metin Gürses

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  1. Metin Gürses
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C. Hoenselaers W. Dietz

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© 1984 Springer-Verlag

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Gürses, M. (1984). Inverse scattering, differential geometry Einstein-Maxwell solitons and one Soliton Bäcklund transformations. In: Hoenselaers, C., Dietz, W. (eds) Solutions of Einstein's Equations: Techniques and Results. Lecture Notes in Physics, vol 205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13366-6_10

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  • DOI: https://doi.org/10.1007/3-540-13366-6_10

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  • Print ISBN: 978-3-540-13366-7

  • Online ISBN: 978-3-540-38922-4

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