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Solitons of Curvature

In: KdV ’95

Author

Listed:
  • B. G. Konopelchenko

    (Università di Lecce e Sezione INFN, Dipartimento di Fisica)

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.

Suggested Citation

  • B. G. Konopelchenko, 1995. "Solitons of Curvature," Springer Books, in: Michiel Hazewinkel & Hans W. Capel & Eduard M. de Jager (ed.), KdV ’95, pages 379-387, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0017-5_21
    DOI: 10.1007/978-94-011-0017-5_21
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