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KdV ’95 pp 379-387 | Cite as

Solitons of Curvature

  • B. G. Konopelchenko

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.

Key words

Gaussian curvature inverse spectral transform 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • B. G. Konopelchenko
    • 1
  1. 1.Dipartimento di FisicaUniversità di Lecce e Sezione INFNLecceItaly

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