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Solitons of Curvature

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KdV ’95

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Abstract

An intristic geometry of surfaces is discussed. In geodesic coordinates the Gauss equation is reduced to the Schrödinger equation where the Gaussian curvature plays the role of a potential. The use of this fact provides an infinite set of explicit expressions for the curvature and metric of a surface. A special case is governed by the KdV equation for the Gaussian curvature. We consider the integrable dynamics of curvature via the KdV equation, higher KdV equations and (2+1)-dimensional integrable equations with breaking solitons.

Mathematics Subject Classifications (1991): 58F07.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Lecce e Sezione INFN, 73100, Lecce, Italy

    B. G. Konopelchenko

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  1. B. G. Konopelchenko
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Michiel Hazewinkel Hans W. Capel Eduard M. de Jager

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© 1995 Springer Science+Business Media Dordrecht

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Konopelchenko, B.G. (1995). Solitons of Curvature. In: Hazewinkel, M., Capel, H.W., de Jager, E.M. (eds) KdV ’95. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0017-5_21

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  • DOI: https://doi.org/10.1007/978-94-011-0017-5_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4011-2

  • Online ISBN: 978-94-011-0017-5

  • eBook Packages: Springer Book Archive

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