Inverse Scattering and the Geroch Group

We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and...

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Published in:arXiv.org
Main Authors: Katsimpouri, Despoina, Kleinschmidt, Axel, Virmani, Amitabh
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 26.09.2013
Subjects:
Algebra
Group theory
Inverse scattering
Linear systems
ISSN:2331-8422
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Abstract We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and we analyse the relation of this group structure to the inverse scattering method of the BZ approach in general. Concrete solution generating methods are exhibited in the BM approach in the so-called soliton transformation sector where the analysis becomes purely algebraic. As a novel example we construct the Kerr-NUT solution by solving the appropriate purely algebraic Riemann-Hilbert problem in the BM approach.
AbstractList We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and we analyse the relation of this group structure to the inverse scattering method of the BZ approach in general. Concrete solution generating methods are exhibited in the BM approach in the so-called soliton transformation sector where the analysis becomes purely algebraic. As a novel example we construct the Kerr-NUT solution by solving the appropriate purely algebraic Riemann-Hilbert problem in the BM approach.
Author Kleinschmidt, Axel
Virmani, Amitabh
Katsimpouri, Despoina
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  surname: Virmani
  fullname: Virmani, Amitabh
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Inverse scattering
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Title Inverse Scattering and the Geroch Group
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